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).

Tenured and tenure-track faculty:

  • Friedlander, Susan (fluid mechanics, partial differential equations)
  • Haydn, Nicolai (dynamical systems, ergodic theory)
  • Jang, Juhi (analysis and PDEs, compressible NSE and Euler equations, kinetic theory, plasma physics, astrophysics)
  • Kukavica, Igor (elliptic and parabolic PDEs, nonlinear dynamics, fluid dynamics, stochastic PDEs, geophysical dynamics)
  • Newton, Paul (theoretical fluid mechanics, nonlinear dynamical systems, and mathematical oncology)
  • Ziane, Mohammed (partial differential equations, geophysical dynamics, Navier-Stokes equations, stochastic PDEs)

Postdoctoral associates:

Activities:

Graduate students:

  • Aydin, Mustafa (partial differential equations, fluid dynamics); advisor: Kukavica
  • Liu, Jiaqi (partial differential equations); advisor: Jang
  • Zhu, Xilu (partial differential equations, harmonic analysis); advisor: Deng

PhD graduates:

  • Malcok, Mehmet (Kukavica), 2001
  • Torres, Juan (Kukavica), 2006
  • Glatt-Holtz, Nathan (Ziane), Stochastic equations in geophysical fluid dynamics, 2008 (currently: Associate Professor, Tulane University)
  • Psiloyenis, Yiannis (Haydn), Mixing conditions and long return times on Markov towers, 2008 (currently: Farmer’s insurance)
  • Vicol, Vlad (Kukavica), Analyticity and Gevrey class regularity for the Euler equations, 2010 (currently: Professor, Courant Institute, NYU)
  • Ignatova, Mihaela (Kukavica), Quantitative unique continuation and complexity of solutions to partial differential equations, 2011 (currently: Assistant Professor, Temple University)
  • 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)
  • Ko, Hong Fu Milton (Haydn), Recurrence and Renyi entropy, 2012 (currently: Business Analyst, Sersys salutations Ltd.)
  • Ostrovskyi, Vitalii (Newton), Point singularities on 2D surfaces, 2013 (currently: Sr. Data Architect, American Express)
  • 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)
  • Pei, Yuan (Kukavica), Certain regularity problems in fluid dynamics, 2014 (currently: Assistant Professor, Western Washington University)
  • 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)
  • Yang, Fan (Haydn) Entry times statistics on metric spaces, 2015 (currently: postdoc, Federal University in Rio de Janeiro)
  • Ugurlu, Kerem (Ziane) Some mathematical problems for the stochastic Navier-Stokes equations, 2016 (currently: Assistant Professor, Nazarbayev University)
  • Wang, Fei (Kukavica) On regularity and stability in fluid dynamics, 2017 (currently: Assistant Professor, Shanghai Jiao Tong University)
  • Camliyurt, Guher 2018 (Kukavica) (currently: Dickson Instructor, University of Chicago)
  • Wang, Weinan 2020 (Kukavica) (currently: postdoc, University of Arizona)
  • Temirgaliyeva, Zhanerke 2020 (Ziane) (currently: lecturer, University of Colorado, Boulder)
  • Rickard, Calum 2020 (Jang) (currently: postdoc University of California, Davis)
  • Wickham, Zachary 2021 (Ziane) (currently: lecturer, Stanford University)
  • Massatt, David 2022 (Kukavica), Global existence, regularity, and asymptotic behavior for nonlinear partial differential equations
  • Park, Jiyeon 2022 (Newton) (currently: postdoc at the University of Utah and City of Hope Cancer Center)
  • Siegel, Maxwell C. 2022 (Kamienny, coadvisor: Haydn)
  • Li, Linfeng 2023 (Jang and Kukavica) (currently: postdoc at UCLA)
  • Park, Gin 2023 (Haydn), Mathematics Instructor, CMS (Creverse, Seoul, So Korea)
  • Wang, Jiakang, 2024 (Haydn), “Some results about random dynamical systems”
  • Le, Quinn, 2024 (Kukavica), “Unique continuation for elliptic and parabolic equations with applications”

Former postdoctoral associates:

  • Do, Tam (partial differential equations, fluid dynamics)
  • Gupta, Chinmaya (dynamical systems)
  • Hu, Weiwei (partial differential equations, control theory)
  • Leslie, Trevor (partial differential equations, fluid dynamics)
  • Nguyen, Trinh (partial differential equations, fluid dynamics)
  • Ozanski, Wojciech (partial differential equations, fluid dynamics)
  • Rusin, Walter (PDEs, fluid dynamics)
  • Ryals, Brian (dynamical systems)
  • Su, Qingtang (dispersive PDE, water waves)
  • Suen, Anthony (partial differential equations, harmonic analysis)
  • Tuffaha, Amjad (PDEs, fluid dynamics)
  • Yue, Haitian (dispersive PDE)
  • Zillinger, Christian (partial differential equations, fluid dynamics)

Archive: