My research, in a broad sense, are in the areas of applied analysis and partial differential equations. My recent interest is more focused on kinetic theory with models arising from physics and biology.
Publications and Preprints:
Mathematical Modelling and Analysis of Fractional Diffusion Induced by Intracellular Noise, W. Sun, M. Tang and X. Xue, submitted, 2019.
Applications of Kinetic Tools to Inverse Transport Problems, Q. Li and W. Sun, accepted, Inverse Problems, 2019.
Multiple Asymptotics of Kinetic Equations with Internal States, B. Perthame, W. Sun, M. Tang, and S. Yasuda, submitted, 2019.
Zero-Diffusion Limit for Aggregation Equations Over Bounded Domains, R. Fetecau, H. Huang, D. Messenger, W. Sun, submitted, 2019.
Uniqueness Of Solutions To A Gas-Disk Interaction System, A. Iatcenko and W. Sun, accepted, ARMA, 2019.
Non-Cutoff Boltzmann Equation with Polynomial Decay Perturbation, R. Alonso, Y. Morimoto, W. Sun, and T. Yang, accepted, Revista Matematica Iberoamericana, 2019.
Propagation of Chaos for the Keller-Segel Equation Over Bounded Domains, R. Fetecau, H. Huang, W. Sun, accepted, JDE 2018.
The Fractional Diffusion Limit of a Kinetic Model with Biochemical Pathway, B. Perthame, W. Sun and M. Tang, accepted, ZAMP, 2018.
Fractional Diffusion Limits of Non-classical Transport Equations , M. Frank and W. Sun, accepted, Kinetic and Related Models, 2018.
Small inertia regularization of an anisotropic aggregation model , J. Evers, R. Fetecau, W. Sun, accepted, M3AS 2017.
Macroscopic Limits of pathway-based kinetic models for E.coli chemotaxis in large gradient environments , W. Sun and M. Tang, accepted, SIAM Multi. Model. Simul., 2016.
A Convergent Method for Linear Half-Space Kinetic Equations , Q. Li, J. Lu, and W. Sun, accepted, M2AN 2016.
Validity and Regularization of Classical Half-Space Equations , Q. Li, J. Lu, and W. Sun, accepted, J. Stat. Phys. 2016.
First-order aggregation models with alignment , R. Fetecau, W. Sun, and C. Tan, accepted, Physica D, 2016.
Half-space kinetic equations with general boundary conditions , Q. Li, J. Lu, and W. Sun, accepted, Math. Comp., 2016.
First-order aggregation models and zero inertia limits , R. Fetecau and W. Sun, accepted, JDE, 2015.
The Radiative Transfer Equation in the Forward-Peaked Regime , R. Alonso and W. Sun, accepted, Comm. Math. Phys. 2015.
Diffusion Approximations of Linear Transport Equations: Asymptotics and Numerics , Q. Li, J. Lu, and W. Sun, accepted, J. Comput. Phys., 2015.
Singular limit of a dispersive Navier-Stokes system with an entropy structure , C. D. Levermore, W. Sun, and K. Trivisa, accepted, Analysis and Applications (2014), DOI: 10.1142/S0219530513500310.
A new numerical method for one dimensional traveling wave simulations . W. Sun and M Tang, Discrete and Continuous Dynamical System-B (2013), no. 5, 1459-1491.
On a singular incompressible porous media equation , S. Friedlander, F. Gancedo, W. Sun, and V. Vicol, Journal of Mathematical Physics 53 (2012), no. 11, 115602, 1-20.
Low Mach number limit of a dispersive Navier-Stokes system , C. David Levermore, W. Sun, and K. Trivisa, SIAM J. Math. Anal., 44(3), (2012) 1760–1807.
Remarks on Oldroyd-B and Related Complex Fluid Models , P. Constantin and W. Sun, Communications in Mathematical Sciences, Vol 10, (2012), 33-73.
Local well-posedness of a dispersive system beyond Navier-Stokes, C. D. Levermore and W. Sun, Indiana Univ. Math. J. 60 (2011), no. 2, 517–576.
Compactness of the gain part of the linearized Boltzmann operator with weakly cutoff kernels , C. D. Levermore and W. Sun, Kinetic and Related Models, Vol 3, Issue 2, (2010), 335-351.