{"id":47,"date":"2019-03-08T11:25:36","date_gmt":"2019-03-08T02:25:36","guid":{"rendered":"http:\/\/mjbae.postech.ac.kr\/?page_id=47"},"modified":"2020-11-06T12:08:24","modified_gmt":"2020-11-06T03:08:24","slug":"research","status":"publish","type":"page","link":"https:\/\/mjbae.postech.ac.kr\/index.php\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n<p>My research interest lies on analysis of nonlinear partial differential  equations. Currently, I am working on free boundary problem with nonlinear  mixed-type PDEs arising from fluid mechanics.  In particular, my recent research is focused on smooth\/non-smooth transonic  flows of Euler system\/Euler-Poisson system.<br>\u3000<\/p>\n\n\n\n<ul><li><strong>Nonlinear PDEs<\/strong><\/li><li><strong>Free boundary problems<\/strong><\/li><li><strong>Mathematical fluid dynamics<\/strong><\/li><\/ul>\n\n\n\n<h2>Papers<\/h2>\n\n\n\n<p><strong>Published <\/strong><\/p>\n\n\n\n<ol><li><em>Structural stability of Supersonic solutions to the Euler-Poisson system&nbsp;<\/em>(with B. Duan, J.-J. Xiao and C. Xie), publihsed online in <strong>Arch. Rat. Mech. Anal<\/strong>. (2020), <a href=\"https:\/\/arxiv.org\/abs\/1602.01892\">arXiv:1602.01892<\/a>&nbsp;<\/li><li>A note on 2-d detached shocks of steady Euler system (with W. Xiang), &nbsp;Proceedings of the HYP2018 conference, <strong>AIMS on Applied Mathematics Vol. 10<\/strong> (2020) 124-135<\/li><li> <em>Contact discontinuities for 3-D axisymmetric inviscid compressible flows in infinitely long cylinders  <\/em>(with&nbsp;H.&nbsp;Park) <em>,<\/em>  <strong>J. Differential Equations<\/strong>, 267(2019) 2824-2873     <\/li><li> <em>Contact discontinuities for 2-D inviscid compressible flows in infinitely long nozzles  <\/em>(with&nbsp;H.&nbsp;Park), <strong>SIMA<\/strong> , 51 no.3 (2019) 1730-1760 <\/li><li><em>Radial transonic shock solutions of Euler-Poisson system in convergent nozzles <\/em> (with&nbsp;Y.&nbsp;Park)<em>,&nbsp;<\/em>&nbsp;<strong>DCDS-S,&nbsp;<\/strong>&nbsp;11&nbsp;no.5(2018)&nbsp;773-791<\/li><li><em>3-D axisymmetric subsonic flows with nonzero swirl for the compressible  Euler-Poisson system&nbsp;<\/em>(with S. Weng), <strong>ANN. I. H. Poincar\u00e8-AN<\/strong>, 35 no.1 (2018) 161-186,  &nbsp;<br><\/li><li><em>Subsonic flow for multidimensional  Euler-Poisson system <\/em><br>(with B. Duan and C. Xie)  <strong>Arch. Rational Mech. Anal. 220 (2016) 155\u2013191<\/strong><br><\/li><li><em>Two dimensional  subsonic flows with self-gravitation in bounded domain<\/em> (with B. Duan and C. Xie)  <strong> Math. Models Methods Appl. Sci.  <\/strong>  <strong>Vol. 25, No. 14 (2015) 2721\u20132747<\/strong><br><\/li><li><em>Subsonic  solutions for steady Euler-Poisson system in two dimensional nozzles<\/em> (with B. Duan and C. Xie)   <strong>SIAM J. Math. Anal.(2014),   &nbsp;46(5),  3455\u20133480<\/strong>\u3000<\/li><li><em>Stability of contact discontinuity for  steady Euler system in infinite duct<\/em><br><strong>Z. Angew. Math. Phys. 64 (2013) pp 917&#8211;936&nbsp;&nbsp;  <\/strong><br><\/li><li><em>Prandtl-Meyer reflection for supersonic flow past a  solid ramp<\/em><br>(with G.-Q. Chen and M. Feldman), <strong>Quart. Appl. Math. (2013) no 3, pp  583&#8211;600<\/strong>\u3000<\/li><li><em>Transonic Shocks in Multi-dimensional Divergent  Nozzles<\/em><br>(with M. Feldman) <strong>Arch. Rat. Mech. Anal., 201(2011), no 3, pp.  777&#8211;840<\/strong><br><\/li><li><em>Regularity of Solutions to Regular Shock  Reflection for Potential Flow<\/em><br>(with G.-Q. Chen and M. Feldman)<strong>  Invent. Math. 175(2009) no 3, pp. 505-543<\/strong><br><br>\u3000<\/li><\/ol>\n\n\n\n<p><strong>Submitted &nbsp;(Mostly available&nbsp;on&nbsp;ArXiv.org)<\/strong><\/p>\n\n\n\n<ol><li><em>Prandtl-Meyer Reflection Configurations, Transonic Shocks, and Free Boundary Problems&nbsp;<\/em>(with G.-Q. Chen and M. Feldman)  , <em>To appear in Memoirs of the AMS <\/em>, <a href=\"https:\/\/arxiv.org\/abs\/1901.05916\">arXiv:1901.05916<\/a>&nbsp;<\/li><li> <em>Detached shock past a blunt body<\/em> (with. W. Xiang) , submitted, <a href=\"https:\/\/arxiv.org\/abs\/1909.13281\">arXiv:1909.13281<\/a><\/li><\/ol>\n\n\n\n<p><strong>In preparation<\/strong><\/p>\n\n\n\n<ol><li>3-D axi-symmetric supersonic solution of Euler-Poisson system  (with H. Park)<\/li><li><em>Transonic shock solutions of Euler-Poisson system <\/em>(with B. Duan and C. Xie)<\/li><li>Smooth transonic flows of Euler-Poisson system(with B. Duan and C. Xie)<\/li><\/ol>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2><strong>(Former) Graduate students<\/strong><\/h2>\n\n\n\n<ul><li><em>Hyangdong Park<\/em> , (Former PhD student at POSTECH, Current position: Postdoc researcher at CMAC, Yonsei University)<\/li><li><em>Hyeongyu Ryu<\/em>, (Current PhD student at POSTECH, PhD thesis defense done on Oct. 23 2020)<\/li><li><em>Yong Park<\/em>,  <br> (Former PhD student at POSTECH, Current position: Wu Wen-Tsun  Assistant professor, Shanghai Jiao Tong University, China) <\/li><li>Heonjin Ha, (Former Master student at POSTECH)<\/li><\/ul>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Are you interested to join my lab? Then, you should&#8230;<\/strong><\/p>\n\n\n\n<ol><li>check my publications and see if they match your research interest&#8230;<\/li><li>check if you took, or are taking the following graduate courses :  <strong><em>Graduate analysis courses (real analysis required, functional analysis, complex analysis recommended) &amp; Graduate level PDE course<\/em><\/strong><\/li><\/ol>\n\n\n\n<h2><strong>(Former) Postdocs<\/strong><\/h2>\n\n\n\n<ul><li><em>Shangkun Weng<\/em> (Former research assistant professor of PMI, currently a  professor at Wuhan University, China)<br><\/li><li><em>Ben Duan&nbsp;<\/em> (Former research assistant professor of PMI, currently a  professor at Dalian University of Technology, China)<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>My research interest lies on analysis of nonlinear partial differential equations. Currently, I am working on free boundary problem with nonlinear mixed-type PDEs arising from fluid mechanics. In particular, my recent research is focused on smooth\/non-smooth transonic flows of Euler system\/Euler-Poisson system.\u3000 Nonlinear PDEs Free boundary problems Mathematical fluid dynamics Papers Published Structural stability of &hellip; <a href=\"https:\/\/mjbae.postech.ac.kr\/index.php\/research\/\" class=\"more-link\"><span class=\"screen-reader-text\">Research<\/span> \ub354\ubcf4\uae30<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/mjbae.postech.ac.kr\/index.php\/wp-json\/wp\/v2\/pages\/47"}],"collection":[{"href":"https:\/\/mjbae.postech.ac.kr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mjbae.postech.ac.kr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mjbae.postech.ac.kr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mjbae.postech.ac.kr\/index.php\/wp-json\/wp\/v2\/comments?post=47"}],"version-history":[{"count":23,"href":"https:\/\/mjbae.postech.ac.kr\/index.php\/wp-json\/wp\/v2\/pages\/47\/revisions"}],"predecessor-version":[{"id":106,"href":"https:\/\/mjbae.postech.ac.kr\/index.php\/wp-json\/wp\/v2\/pages\/47\/revisions\/106"}],"wp:attachment":[{"href":"https:\/\/mjbae.postech.ac.kr\/index.php\/wp-json\/wp\/v2\/media?parent=47"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}