Timur Yastrzhembskiy

I am an Assistant Research Fellow at the Institute of Mathematics, Academia Sinica, Taiwan. 

I obtained my Ph.D. at the University of Minnesota in May 2020 under the supervision of Prof. Nicolai V. Krylov. 

Previously, I was a Van Vleck Visiting Assistant Professor of Mathematics at University of Wisconsin-Madison 2024-2025, mentored by Prof. Dallas Albritton.  Before that, I was a Prager Assistant Professor of Applied Mathematics 2020-2023 and a Visiting Lecturer in Applied Mathematics at Brown University 2023-2024, mentored by Profs. Hongjie Dong and Yan Guo. 

My research interests are kinetic theory and partial differential equations.

Email: yastr at as.edu.tw 

Papers

• Asymptotic Stability for Relativistic Vlasov-Maxwell-Landau System in Bounded Domain (with Hongjie Dong and Yan Guo), 2024, submitted. The new version includes a global well-posedness result. Further improvements are as follows: enhanced control of instant energies, more precise decay estimates of instant energies, and a significantly improved presentation. The manuscript now comprises 99 pages.

• Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations (with Hongjie Dong), Advanced Nonlinear Studies, 2025. https://doi.org/10.1515/ans-2023-0167

• The Local-well-posedness of the relativistic Vlasov-Maxwell-Landau system with the specular reflection boundary condition (with Hongjie Dong, Yan Guo, and Zhimeng Ouyang), SIAM J. Math. Anal. 56 (2024), no. 5, 6613-6688.

• Global L_p estimates for kinetic Kolmogorov-Fokker-Planck equations in divergence form (with Hongjie Dong), SIAM J. Math. Anal. 2024 56:1, 1223-1263.

• Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition (with Yan Guo and Hongjie Dong), Kinetic &Related Models 15 (2022), no. 3, 467-516.

• Global L_p estimates for kinetic Kolmogorov-Fokker-Planck equations in nondivergence form (with Hongjie Dong), Arch. Ration. Mech. Anal. 245 (2022), no. 1, 501-564.

• Support theorem for an SPDE with multiplicative noise driven by a cylindrical Wiener process on the real line, Stoch. Partial Differ. Equ. Anal. Comput. 9 (2021), no. 1, 71–104.

• Wong-Zakai approximation and support theorem for semilinear stochastic partial differential equations with finite dimensional noise in the whole space,  Stoch. Partial Differ. Equ. Anal. Comput. 8 (2020), no. 3, 509-543.

• On nonequivalence of regular boundary points for second-order elliptic operators (with Nicolai V. Krylov), Comm. PDE 42 (2017), no. 3, 366-387.

• A note on the strong Feller property of diffusion processes, arXiv:2001.09919v1 (2019),

• On the l_p stability estimates for stochastic and deterministic difference equations and their application to SPDEs and PDEs,  arXiv:1910.13640v1

Talks

• Workshop on Kinetic Theory and Fluids, UW-Madison, March 29, 2025.

• Colloquium talk at the Institute of Mathematics, Academia Sinica, January 3, 2024 (virtual).

• PDE seminar, Brown University, December 15, 2023.

• PDE and Geometric Analysis seminar, UW-Madison, December 11, 2023.

• PDE and Applied Mathematics seminar, UC Davis, October 26, 2023 (virtual).

• 2023 Fall AMS Southeastern Sectional Meeting, special session on Dynamics of Fluids, University of South Alabama, October 13-15.

• 2022 Fall AMS Southeastern Sectional Meeting, special session on Nonstandard Elliptic and Parabolic Regularity Theory with Applications, University of Tennessee at Chattanooga, October 15-16
• Analysis of Fluids and Related Topics seminar, Princeton University, October 6, 2022.

• Analysis seminar, March 14th, Brown University, 2022.

• Virtual analysis and PDE seminar, January 13th, 2022.

• Non-local operators, probability,  and singularities, June 1st, 2021.

• PDE seminar, Brown University, November 20th, 2020.

• RISM School on Developments in Stochastic Partial Differential Equations in honor of Giuseppe Da Prato, 07/26/2018, Varese, Italy (short talk).

• PDE seminar, University of Minnesota, April 27th, 2016.