My main research interest lies in PDE models that arise in plasma theory, fluid dynamics, quantum mechanics, etc.. Examples include the relativistic Vlasov-Maxwell equation, the Vlasov-Poisson equation, the nonlinear Schrödinger equation, the Benjamin-Ono equation, the Navier-Stokes equation, etc.. In particular, I have been working on the construction and the stability properties of special solutions of these equations, such as equilibria and solitary waves, as well as blow-up-like behavior of the solutions. 

In general, I am open to exploring a wide variety of PDE models, especially kinetic theory, fluid models as well as dispersive equations. 

Here is my Google Scholar page.

Publications and Preprints

1. Linear Stability Analysis of the Relativistic Vlasov-Maxwell System in an Axisymmetric Domain, SIAM Journal on Mathematical Analysis, 51(6), 4683-4723

2. Focusing Solutions of the Vlasov-Poisson System, Kinetic and Related Models, December 2019, Vol. 12, No. 6, 1313-1327

3. Benjamin-Ono Soliton Dynamics in a Slowly Varying Potential, Nonlinearity, March 2020, 33(3), 1064-1093

4. Stationary Flows for Compressible Viscous Fluid in a Perturbed Half-Space, with Masahiro Suzuki, Communications in Mathematical Physics, 388, no. 3 (2021): 1131-1180

5. Magnetic Confinement at a Boundary Approximates Specular Reflection, Mathematical Methods in the Applied Sciences, 44, no. 7 (2021): 5705-5738

6. Boundary Layers of the Boltzmann Equation in a Three-Dimensional Half-Space, with Shota Sakamoto and Masahiro Suzuki, Journal of Differential Equations, 314 (2022): 446-472

7. Benjamin-Ono Soliton Dynamics in a Slowly Varying Potential Revisited, with Justin Holmer, SIAM Journal on Mathematical Analysis, 54, no. 2 (2022): 2634-2690 

8. Effective Dynamics of the Vector Nonlinear Schrödinger Equations on Large Domains, Journal of Mathematical Analysis and Applications, 517, no. 2 (2023): 126636

9. On 1d Quadratic Klein-Gordon Equations with a Potential and Symmetries, with Pierre Germain and Fabio Pusateri, Archive for Rational Mechanics and Analysis,  247, no. 2 (2023): 17

10. Solutions of the 2D Radially Symmetric Vlasov-Maxwell System with an Initial Focusing Phase, Kinetic and Related Models (2023): 16(6), 871-883

11. Nonlinear Stability and Instability of Plasma Boundary Layers, with Masahiro Suzuki and Masahiro Takayama, preprint arXiv:2208.07326 

12. Continuous Family of Equilibria of the 3D Axisymmetric Relativistic Vlasov-Maxwell System, Journal of Differential Equations, 374 (2023): 279-315

13. Traveling Waves of the Vlasov-Poisson System, with Masahiro Suzuki and Masahiro Takayama, preprint arXiv:2306.13459 

14. Local Well-posedness for the Kinetic MMT Model, with Pierre Germain and Joonhyun La, Communications in Mathematical Physics 406, no. 1 (2025): 1-38

15. On the Ground State of One-Dimensional Quantum Droplets for Large Chemical Potentials, with Justin Holmer and Panayotis G. Kevrekidis, 2024 J. Phys. A: Math. Theor. 57 445701  

16. Stationary Flows for Viscous Heat-Conductive Fluid in a Perturbed Half-Space, with Mingjie Li and Masahiro Suzuki, preprint arXiv:2410.14511