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:**

*Propagation of Chaos for the Keller-Segel Equation Over Bounded Domains* (with R. Fetecau and H. Huang), submitted, *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.** *

*Links:*