{"id":23504,"date":"2023-04-18T08:28:53","date_gmt":"2023-04-17T23:28:53","guid":{"rendered":"https:\/\/www.waseda.jp\/inst\/sgu\/?p=23504"},"modified":"2023-04-18T08:37:01","modified_gmt":"2023-04-17T23:37:01","slug":"study-abroad-report-taiki-takeuchi-paderborn-university-and-leibniz-university-hannover-germany","status":"publish","type":"post","link":"https:\/\/www.waseda.jp\/inst\/sgu\/news-en\/2023\/04\/18\/23504\/","title":{"rendered":"Study Abroad Report: Taiki Takeuchi &#8211; \u201cPaderborn University\u201d and \u201cLeibniz University Hannover\u201d (Germany)"},"content":{"rendered":"<h3>Taiki TAKEUCHI (2nd year Doctor\u2019s student, Department of Pure and Applied Mathematics)<\/h3>\n<h4>1. Destination<\/h4>\n<p>\u201cPaderborn University\u201d and \u201cLeibniz University Hannover\u201d (Germany)<\/p>\n\n\t\t<style type=\"text\/css\">\n\t\t\t#gallery-1 {\n\t\t\t\tmargin: auto;\n\t\t\t}\n\t\t\t#gallery-1 .gallery-item {\n\t\t\t\tfloat: left;\n\t\t\t\tmargin-top: 10px;\n\t\t\t\ttext-align: center;\n\t\t\t\twidth: 50%;\n\t\t\t}\n\t\t\t#gallery-1 img {\n\t\t\t\tborder: 2px solid #cfcfcf;\n\t\t\t}\n\t\t\t#gallery-1 .gallery-caption {\n\t\t\t\tmargin-left: 0;\n\t\t\t}\n\t\t\t\/* see gallery_shortcode() in wp-includes\/media.php *\/\n\t\t<\/style>\n\t\t<div id='gallery-1' class='gallery galleryid-23504 gallery-columns-2 gallery-size-thumbnail'><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/www.waseda.jp\/inst\/sgu\/news-en\/2023\/04\/18\/23504\/attachment\/paderborn-university\/'><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"270\" src=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/Paderborn-University-360x270.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-23517\" srcset=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/Paderborn-University-360x270.jpg 360w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/Paderborn-University.jpg 562w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-23517'>\n\t\t\t\tPaderborn University\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/www.waseda.jp\/inst\/sgu\/news-en\/2023\/04\/18\/23504\/attachment\/leibniz-university-hannover\/'><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"270\" src=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/Leibniz-University-Hannover-360x270.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-23516\" srcset=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/Leibniz-University-Hannover-360x270.jpg 360w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/Leibniz-University-Hannover-610x457.jpg 610w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/Leibniz-University-Hannover.jpg 642w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-23516'>\n\t\t\t\tLeibniz University Hannover\n\t\t\t\t<\/dd><\/dl><br style=\"clear: both\" \/>\n\t\t<\/div>\n\n<h4>2. Period of Stay<\/h4>\n<p>From January 30, 2023 to March 15, 2023 (44 days)<\/p>\n<h4>3. Purpose<\/h4>\n<h3>Paderborn University<\/h3>\n<p>To visit Prof. Michael Winkler and his research group for studying the mathematical analysis of the chemotaxis system and obtaining the opportunity to conduct joint research.<\/p>\n<h3>Leibniz University Hannover<\/h3>\n<p>To participate in the international research conference \u201cThe 6th International Workshop on Mathematical Analysis of Chemotaxis (iWMAC6)\u201d and give a presentation on my research results.<\/p>\n<p>(URL:<a href=\"https:\/\/www.ifam.uni-hannover.de\/en\/iwmac6\"> https:\/\/www.ifam.uni-hannover.de\/en\/iwmac6<\/a>)<\/p>\n<h4>4. Host Professor<\/h4>\n<p>Prof. Michael Winkler (Paderborn University)<\/p>\n<h4>5. Research Activity<\/h4>\n<p>Firstly, I participated in the international research conference \u201ciWMAC6\u201d and gave a presentation:<\/p>\n<table style=\"width: 100%; border-collapse: collapse; height: 24px;\" border=\"1\">\n<tbody>\n<tr style=\"height: 24px;\">\n<td style=\"width: 100%; height: 24px;\"><span style=\"text-decoration: underline;\">T. Takeuchi,<\/span> \u201cVanishing viscosity method for the Keller-Segel-Navier-Stokes system\u201d, the 6th International Workshop on the Mathematical Analysis of Chemotaxis, Leibniz University Hannover, Feb. 13, 2023 (Invited).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Secondly, I studied the Keller-Segel-Navier-Stokes system with nonlinear boundary conditions. Precisely, for the usual Keller-Segel-Navier-Stokes system, the cell density n and the concentration of the chemo-attractant c satisfy the Neumann boundary conditions \u2207n\u2219\u03bd=\u2207c\u2219\u03bd=0. However, recently, Xue and Othmer (SIAM J. Appl. Math. 70 (2009), no. 1, 133\u2014167) derived a new model such that the boundary condition of the cell density n is given by the nonlinear terms \u2207n\u2219\u03bd=nS\u2207c\u2219\u03bd. For this model, Prof. Winkler has given some mathematical results from the viewpoint of the functional equation (J. Evol. Equ. 18 (2018), no. 3, 1267\u20141289 and Int. Math. Res. Not. IMRN (2021), no. 11, 8106\u20148152). On the other hand, I showed the existence and uniqueness of global strong solutions of the system based on the maximal regularity theorem. Here, the most important point is how to deal with the nonlinear boundary condition \u2207n\u2219\u03bd=nS\u2207c\u2219\u03bd. In contrast to the previous results, I obtained the solutions directly without considering the approximation system.<\/p>\n<p>Finally, by the above result, I obtained the opportunity to conduct joint research with Dr. Frederic Heihoff, who is a young researcher in Prof. Winkler\u2019s group. Here, the aim of our joint research is to establish a new blow-up criterion of the system. Because I obtained the solutions with the initial data in Besov spaces, we expect that another blow-up criterion will be shown in the Besov spaces framework. This is still work in progress, so I will continue to consider the problems.<\/p>\n\n\t\t<style type=\"text\/css\">\n\t\t\t#gallery-2 {\n\t\t\t\tmargin: auto;\n\t\t\t}\n\t\t\t#gallery-2 .gallery-item {\n\t\t\t\tfloat: left;\n\t\t\t\tmargin-top: 10px;\n\t\t\t\ttext-align: center;\n\t\t\t\twidth: 50%;\n\t\t\t}\n\t\t\t#gallery-2 img {\n\t\t\t\tborder: 2px solid #cfcfcf;\n\t\t\t}\n\t\t\t#gallery-2 .gallery-caption {\n\t\t\t\tmargin-left: 0;\n\t\t\t}\n\t\t\t\/* see gallery_shortcode() in wp-includes\/media.php *\/\n\t\t<\/style>\n\t\t<div id='gallery-2' class='gallery galleryid-23504 gallery-columns-2 gallery-size-thumbnail'><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/www.waseda.jp\/inst\/sgu\/news-en\/2023\/04\/18\/23504\/attachment\/during-iwmac6-in-hannover\/'><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"270\" src=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/During-iWMAC6-in-Hannover-360x270.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-2-23526\" srcset=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/During-iWMAC6-in-Hannover-360x270.jpg 360w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/During-iWMAC6-in-Hannover.jpg 529w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-2-23526'>\n\t\t\t\tDuring \u201ciWMAC6\u201d in Hannover\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/www.waseda.jp\/inst\/sgu\/news-en\/2023\/04\/18\/23504\/attachment\/with-prof-michael-winkler-2\/'><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"270\" src=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/With-Prof.-Michael-Winkler-1-360x270.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-2-23527\" srcset=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/With-Prof.-Michael-Winkler-1-360x270.jpg 360w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/With-Prof.-Michael-Winkler-1-610x458.jpg 610w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/04\/With-Prof.-Michael-Winkler-1.jpg 642w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-2-23527'>\n\t\t\t\tWith Prof. Michael Winkler\n\t\t\t\t<\/dd><\/dl><br style=\"clear: both\" \/>\n\t\t<\/div>\n\n<h4>6. Other comments<\/h4>\n<p>I would like to express my appreciation for Prof. Michael Winkler for accepting my research visit. In addition, I am truly honored to be able to see and discuss him face-to-face. By the discussion, I could obtain the opportunity to conduct joint research with a young researcher in Paderborn. During my stay in Paderborn, young researchers kindly helped me a lot, mainly around university procedures and life in Germany. Thanks to them, I could really enjoy spending time in Paderborn until the end.<\/p>\n<p>Concerning the international research conference \u201ciWMAC6\u201d in Hannover, I would like to thank the organizers; Dr. Johannes Lankeit, Dr. Sachiko Ishida, Dr. Masaaki Mizukami, and Dr. Mario Fuest. By virtue of the invitation, I could go through the first experience of giving a presentation in the international conference held overseas. During the conference, I could talk to a lot of international researchers from not only Germany but also Austria, China, Poland, Italy, Korea, Poland, and the United Kingdom. And then I could enjoy many kinds of nice German foods with them during dinner time in Hannover, so I could have a wonderful experience in various aspects.<\/p>\n\n\t\t<style type=\"text\/css\">\n\t\t\t#gallery-3 {\n\t\t\t\tmargin: auto;\n\t\t\t}\n\t\t\t#gallery-3 .gallery-item {\n\t\t\t\tfloat: left;\n\t\t\t\tmargin-top: 10px;\n\t\t\t\ttext-align: center;\n\t\t\t\twidth: 33%;\n\t\t\t}\n\t\t\t#gallery-3 img {\n\t\t\t\tborder: 2px solid #cfcfcf;\n\t\t\t}\n\t\t\t#gallery-3 .gallery-caption {\n\t\t\t\tmargin-left: 0;\n\t\t\t}\n\t\t\t\/* see gallery_shortcode() in wp-includes\/media.php *\/\n\t\t<\/style>\n\t\t<div id='gallery-3' class='gallery galleryid-23504 gallery-columns-3 gallery-size-thumbnail'><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/www.waseda.jp\/inst\/sgu\/news-through-2023\/2023\/04\/03\/23144\/attachment\/s__211615746\/'><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"270\" src=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615746-360x270.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" srcset=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615746-360x270.jpg 360w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615746-610x457.jpg 610w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615746-940x705.jpg 940w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615746-768x576.jpg 768w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615746-720x540.jpg 720w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615746.jpg 1479w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>\n\t\t\t<\/dt><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/www.waseda.jp\/inst\/sgu\/news-through-2023\/2023\/04\/03\/23144\/attachment\/s__211615750\/'><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"270\" src=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615750-360x270.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" srcset=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615750-360x270.jpg 360w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615750-610x457.jpg 610w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615750-940x705.jpg 940w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615750-768x576.jpg 768w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615750-720x540.jpg 720w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615750.jpg 1479w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>\n\t\t\t<\/dt><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/www.waseda.jp\/inst\/sgu\/news-through-2023\/2023\/04\/03\/23144\/attachment\/s__211615748\/'><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"270\" src=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615748-360x270.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" srcset=\"https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615748-360x270.jpg 360w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615748-610x457.jpg 610w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615748-940x705.jpg 940w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615748-768x576.jpg 768w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615748-720x540.jpg 720w, https:\/\/www.waseda.jp\/inst\/sgu\/assets\/uploads\/2023\/03\/S__211615748.jpg 1479w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>\n\t\t\t<\/dt><\/dl><br style=\"clear: both\" \/>\n\t\t<\/div>\n\n<p>Lastly, I am deeply indebted to Prof. Hideo Kozono and Top Global University Project in Waseda University for giving me the important opportunity to visit Paderborn and Hannover. I am also thankful to Ms. Yukari Ishizaki for a permission request and an office procedure around the research visit.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Taiki TAKEUCHI (2nd year Doctor\u2019s student, Department of Pure and Applied Mathematics) 1. Destination \u201cPaderbo [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":23517,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[18],"tags":[109,111],"class_list":["post-23504","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news-en","tag-en-mams","tag-report-en"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.waseda.jp\/inst\/sgu\/wp-json\/wp\/v2\/posts\/23504","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.waseda.jp\/inst\/sgu\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.waseda.jp\/inst\/sgu\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/inst\/sgu\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/inst\/sgu\/wp-json\/wp\/v2\/comments?post=23504"}],"version-history":[{"count":3,"href":"https:\/\/www.waseda.jp\/inst\/sgu\/wp-json\/wp\/v2\/posts\/23504\/revisions"}],"predecessor-version":[{"id":23608,"href":"https:\/\/www.waseda.jp\/inst\/sgu\/wp-json\/wp\/v2\/posts\/23504\/revisions\/23608"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/inst\/sgu\/wp-json\/wp\/v2\/media\/23517"}],"wp:attachment":[{"href":"https:\/\/www.waseda.jp\/inst\/sgu\/wp-json\/wp\/v2\/media?parent=23504"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.waseda.jp\/inst\/sgu\/wp-json\/wp\/v2\/categories?post=23504"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.waseda.jp\/inst\/sgu\/wp-json\/wp\/v2\/tags?post=23504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}