{"id":183,"date":"2023-01-14T16:15:22","date_gmt":"2023-01-15T00:15:22","guid":{"rendered":"https:\/\/dornsife.usc.edu\/mathematics\/?page_id=183"},"modified":"2025-10-21T18:04:35","modified_gmt":"2025-10-22T01:04:35","slug":"analysis-and-differential-equations","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/mathematics\/analysis-and-differential-equations\/","title":{"rendered":"Analysis and Differential Equations"},"content":{"rendered":"\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p> The analysis\/differential equations group conducts research in theory and applications of ordinary and partial differential equations and dynamical systems. The areas of research include: differential equations (ODEs and PDEs), difference equations, dynamical systems, ergodic theory, fluid dynamics, long time behavior of dynamical systems, modeling in mathematical biology, nonlinear PDEs and applications, stochastic ODEs and PDEs, fluid dynamics (Navier-Stokes, Euler, and Boussinesq equations).<\/p>\n<h4><\/h4>\n<h4>Tenured and tenure-track faculty:<\/h4>\n<ul>\n<li><a href=\"https:\/\/dornsife.usc.edu\/friedlander-susan\/\" target=\"_blank\" rel=\"noopener\">Friedlander, Susan<\/a> (fluid mechanics, partial differential equations)<\/li>\n<li><a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\" target=\"_blank\" rel=\"noopener\">Haydn, Nicolai<\/a> (dynamical systems, ergodic theory)<\/li>\n<li><a title=\"https:\/\/dornsife.usc.edu\/profile\/juhi-jang\" href=\"https:\/\/dornsife.usc.edu\/juhijang\" target=\"_blank\" rel=\"noopener\">Jang, Juhi<\/a> (analysis and PDEs, compressible NSE and Euler equations, kinetic theory, plasma physics, astrophysics)<\/li>\n<li><a title=\"https:\/\/dornsife.usc.edu\/profile\/igor-kukavica\" href=\"https:\/\/dornsife.usc.edu\/igor-kukavica\/\" target=\"_blank\" rel=\"noopener\">Kukavica, Igor<\/a> (elliptic and parabolic PDEs, nonlinear dynamics, fluid dynamics, stochastic PDEs, geophysical dynamics)<\/li>\n<li><a href=\"https:\/\/newton.usc.edu\" target=\"_blank\" rel=\"noopener\">Newton, Paul<\/a> (theoretical fluid mechanics, nonlinear dynamical systems, and mathematical oncology)<\/li>\n<li><a href=\"https:\/\/dornsife.usc.edu\/profile\/nabil-ziane\">Ziane, Mohammed<\/a> (partial differential equations, geophysical dynamics, Navier-Stokes equations, stochastic PDEs)<\/li>\n<\/ul>\n<p><!--<\/ul>\n\n\n\n\n<h4><\/h4>\n\n\n\n\n<h4>Retired faculty:<\/h4>\n\n\n\n\n<ul>\n \t\n\n<li><a title=\"https:\/\/dornsife.usc.edu\/profile\/robert-sacker\" href=\"https:\/\/dornsife.usc.edu\/robert-sacker\" target=\"_blank\" rel=\"noopener\">Sacker, Robert<\/a> (ordinary differential equations, difference equations, infinite dimensional dynamical systems, applied mathematics, mathematical biology)<\/li>\n\n\n<\/ul>\n\n\n--><\/p>\n<h4><\/h4>\n<h4>Postdoctoral associates:<\/h4>\n<ul>\n<li><a href=\"https:\/\/dornsife.usc.edu\/profile\/abhishek-balakrishna\" target=\"_blank\" rel=\"noopener\">Balakrishna, Abhishek<\/a> (partial differential equations, fluid dynamics)<\/li>\n<\/ul>\n<h4><\/h4>\n<h4>Activities:<\/h4>\n<ul>\n<li>joint Caltech\/UCLA\/USC Seminar<\/li>\n<li><a href=\"https:\/\/dornsife.usc.edu\/cams\/colloquia\/\">CAMS Colloquium<\/a><\/li>\n<li><a title=\"Graduate Analysis\/PDE seminar\" href=\"https:\/\/ikukavica.dreamhosters.com\/graduate_seminar.html\">Graduate Analysis\/PDE seminar<\/a><\/li>\n<li>Analysis\/PDE seminar<\/li>\n<\/ul>\n<h4><\/h4>\n<h4>Graduate students:<\/h4>\n<ul>\n<li>Aydin, Mustafa (partial differential equations, fluid dynamics); advisor: Kukavica<\/li>\n<li>Cao, Han (partial differential equations); advisor: Jang<\/li>\n<li>Ingimarson, Benjamin (partial differential equations, fluid dymaics); advisor: Kukavica <\/li>\n<li>Liu, Jiaqi (partial differential equations); advisor: Jang<\/li>\n<li>Wang, Qimin (partial differential equations, fluid dynamics); advisor: Ziane<\/li>\n<li>Xu, Qi (partial differential equations, fluid dymaics); advisor: Kukavica <\/li>\n<\/ul>\n<h4><\/h4>\n<h4>PhD graduates:<\/h4>\n<ul>\n<li>Malcok, Mehmet (Kukavica), 2001<\/li>\n<li>Torres, Juan (Kukavica), 2006<\/li>\n<li>Glatt-Holtz, Nathan (Ziane), Stochastic equations in geophysical fluid dynamics, 2008 (currently: Professor, Indiana University)<\/li>\n<li>Psiloyenis, Yiannis (Haydn), Mixing conditions and long return times on Markov towers, 2008 (currently: Farmer&#8217;s insurance)<\/li>\n<li><a href=\"https:\/\/cims.nyu.edu\/~vicol\/\">Vicol, Vlad<\/a> (Kukavica), Analyticity and Gevrey class regularity for the Euler equations, 2010 (currently: Professor, Courant Institute, NYU)<\/li>\n<li><a href=\"https:\/\/math.temple.edu\/~tuk46086\/\">Ignatova, Mihaela<\/a> (Kukavica), Quantitative unique continuation and complexity of solutions to partial differential equations, 2011 (currently: Associate Professor, Temple University)<\/li>\n<li>Reis, Ednei (Kukavica), Asymptotic expansion for solutions of the Navier-Stokes equations with potential forces, 2011 (currently: Professor Adjunto, Universidade tecnologica federal do Parana, Brasil)<\/li>\n<li>Ko, Hong Fu Milton (Haydn), Recurrence and Renyi entropy, 2012 (currently: Business Analyst, Sersys salutations Ltd.)<\/li>\n<li>Ostrovskyi, Vitalii (Newton), Point singularities on 2D surfaces, 2013 (currently: Sr. Data Architect, American Express)<\/li>\n<li>Williams, Katarzyna (Haydn), Limiting distribution and error terms for the number of visits to balls in mixing dynamical systems, 2013 (currently: teacher, Harvard-Westlake school)<\/li>\n<li><a href=\"https:\/\/mathematics.wwu.edu\/people\/peiy\">Pei, Yuan<\/a> (Kukavica), Certain regularity problems in fluid dynamics, 2014 (currently: Associate Professor, Western Washington University)<\/li>\n<li>Garcia-Torres (Banuelos), Selenne (Sacker) Structured two-stage population model with migration between multiple patches in a periodic environment, 2013 (currently: Assistant Professor, CSU Channel Islands)<\/li>\n<li>Yang, Fan (Haydn) Entry times statistics on metric spaces, 2015 (currently: postdoc, Federal University in Rio de Janeiro)<\/li>\n<li>Ugurlu, Kerem (Ziane) Some mathematical problems for the stochastic Navier-Stokes equations, 2016 (currently: Assistant Professor, Nazarbayev University)<\/li>\n<li>Wang, Fei (Kukavica) On regularity and stability in fluid dynamics, 2017 (currently: Assistant Professor, Shanghai Jiao Tong University)<\/li>\n<li><a href=\"https:\/\/math.vt.edu\/people\/faculty\/camliyurt-guher.html\">Camliyurt, Guher <\/a> 2018 (Kukavica) (currently: Assistant Professor, Virginia Tech)<\/li>\n<li><a href=\"https:\/\/sites.google.com\/view\/weinanwang\/home\">Wang, Weinan<\/a> 2020 (Kukavica) (currently: Assistant Professor, University of Oklahoma)<\/li>\n<li>Temirgaliyeva, Zhanerke 2020 (Ziane) (currently: lecturer, University of Colorado, Boulder)<\/li>\n<li><a href=\"https:\/\/sites.google.com\/view\/calumrickard\/teaching\">Rickard, Calum<\/a> 2020 (Jang) (currently: instructor, University of Southern California)<\/li>\n<li>Wickham, Zachary 2021 (Ziane) (currently: lecturer, Stanford University)<\/li>\n<li>Massatt, David 2022 (Kukavica), Global existence, regularity, and asymptotic behavior for nonlinear partial differential equations<\/li>\n<li>Park, Jiyeon 2022 (Newton) (currently: postdoc at the University of Utah and City of Hope Cancer Center)<\/li>\n<li>Siegel, Maxwell C. 2022 (Kamienny, coadvisor: Haydn)<\/li>\n<li>Li, Linfeng 2023 (Jang and Kukavica) (currently: Hedrick Assistant Adjunct Professor at UCLA)<\/li>\n<li>Park, Gin 2023 (Haydn), Mathematics Instructor, CMS (Creverse, Seoul, So Korea)<\/li>\n<li>Wang, Jiakang, 2024 (Haydn), &#8220;Some results about random dynamical systems&#8221;<\/li>\n<li>Le, Quinn, 2024 (Kukavica), &#8220;Unique continuation for elliptic and parabolic equations with applications&#8221;<\/li>\n<li>Zhu, Xilu, 2025 (Deng) <\/li>\n<\/ul>\n<h4><\/h4>\n<h4>Former postdoctoral associates:<\/h4>\n<ul>\n<li>Do, Tam (partial differential equations, fluid dynamics)<\/li>\n<li>Gupta, Chinmaya (dynamical systems)<\/li>\n<li>Hu, Weiwei (partial differential equations, control theory)<\/li>\n<li>Jayanti, Pranava Chaitanya (partial differential equations, fluid dynamics)<\/li>\n<li>Leslie, Trevor (partial differential equations, fluid dynamics)<\/li>\n<li>Nguyen, Trinh (partial differential equations, fluid dynamics)<\/li>\n<li>Ozanski, Wojciech (partial differential equations, fluid dynamics)<\/li>\n<li>Rusin, Walter (PDEs, fluid dynamics)<\/li>\n<li>Ryals, Brian (dynamical systems)<\/li>\n<li>Su, Boyang (dispersive PDEs)<\/li>\n<li>Su, Qingtang (dispersive PDE, water waves)<\/li>\n<li>Suen, Anthony (partial differential equations, harmonic analysis)<\/li>\n<li>Tuffaha, Amjad (PDEs, fluid dynamics)<\/li>\n<li>Yue, Haitian (dispersive PDE)<\/li>\n<li>Zillinger, Christian (partial differential equations, fluid dynamics)<\/li>\n<\/ul>\n<h4><\/h4>\n<h4>Archive:<\/h4>\n<ul>\n<li><a title=\"2019 Summer School\" href=\"math.usc.edu\/summer-school-on-recent-advances-in-mathematical-fluid-dynamics-may-20-24-2019\/\">Summer School on Recent Advances in Mathematical Fluid Dynamics, May 20-24, 2019<\/a><\/li>\n<li><a href=\"https:\/\/dornsife.usc.edu\/juhijang\/usc-summer-school-on-mathematical-fluids\/\">2017 USC Summer School on Mathematical Fluids<\/a><\/li>\n<\/ul>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":279,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-183","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Analysis and Differential Equations - Department of Mathematics<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/mathematics\/analysis-and-differential-equations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Analysis and Differential Equations - Department of Mathematics\" \/>\n<meta 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