My research, in a broad sense, are in the areas of applied analysis and partial differential equations. In particular, I am interested in kinetic theory and fluid mechanics, including complex fluids. My recent work has been more focused on kinetic equations. Some specific topics are well-posedness of kinetic equations, boundary layer analysis, and moment-system approximations.
Publications and Preprints:
Zero-Diffusion Limit for Aggregation Equations Over Bounded Domains (with R. Fetecau, H. Huang, and D. Messenger), submitted, 2018.
Propagation of Chaos for the Keller-Segel Equation Over Bounded Domains (with R. Fetecau and H. Huang), accepted, JDE 2018.
The Fractional Diffusion Limit of a Kinetic Model with Biochemical Pathway (with B. Perthame and M. Tang), accepted, ZAMP, 2018.
Fractional Diffusion Limits of Non-classical Transport Equations (with M. Frank), accepted, Kinetic and Related Models, 2018.
Small inertia regularization of an anisotropic aggregation model (with J. Evers and R. Fetecau), accepted, M3AS 2017.
Macroscopic Limits of pathway-based kinetic models for E.coli chemotaxis in large gradient environments (with M. Tang), accepted, SIAM Multi. Model. Simul., 2016.
A Convergent Method for Linear Half-Space Kinetic Equations (with Q. Li and J. Lu), accepted, M2AN 2016.
Validity and Regularization of Classical Half-Space Equations (with Q. Li and J. Lu), accepted, J. Stat. Phys. 2016.
First-order aggregation models with alignment (with R. Fetecau and C. Tan), accepted, Physica D, 2016.
Half-space kinetic equations with general boundary conditions (with Q. Li and J. Lu), accepted, Math. Comp., 2016.
First-order aggregation models and zero inertia limits (with R. Fetecau), accepted, JDE, 2015.
The Radiative Transfer Equation in the Forward-Peaked Regime (with R. Alonso), accepted, Comm. Math. Phys. 2015.
Diffusion Approximations of Linear Transport Equations: Asymptotics and Numerics (with Q. Li and J. Lu), accepted, J. Comput. Phys., 2015.
Singular limit of a dispersive Navier-Stokes system with an entropy structure (with C. David Levermore and Konstantina Trivisa), accepted, Analysis and Applications (2014), DOI: 10.1142/S0219530513500310.
A new numerical method for one dimensional traveling wave simulations (with Min Tang), Discrete and Constinuous Dynamical System-B (2013), no. 5, 1459-1491.
On a singular incompressible porous media equation (with Susan Friedlander, Francisco Gancedo, and Vlad Vicol), Journal of Mathematical Physics 53 (2012), no. 11, 115602, 1-20.
Low Mach number limit of a dispersive Navier-Stokes system (with C. David Levermore and Konstantina Trivisa), SIAM J. Math. Anal., 44(3), (2012) 1760–1807.
Remarks on Oldroyd-B and Related Complex Fluid Models (with Peter Constantin), Communications in Mathematical Sciences, Vol 10, (2012), 33-73.
Local well-posedness of a dispersive system beyond Navier-Stokes (with C. David Levermore), Indiana Univ. Math. J. 60 (2011), no. 2, 517–576.
Compactness of the gain part of the linearized Boltzmann operator with weakly cutoff kernels (with C. David Levermore), Kinetic and Related Models, Vol 3, Issue 2, (2010), 335-351.