arXiv subjects
Publications and source records attributed to Yingshan Chen.
In this paper we obtain all doubly-stochastic solutions to the Yang-Baxter-like matrix equation $AXA = XAX$ when $A$ is a permutation matrix. We characterize the permutation solutions, proper doubly stochastic solutions, and we accompany our results with suitable examples.
In this paper, we consider the Cauchy problem for a compressible Oldroyd-B model in three dimensions. Under some smallness assumptions on the initial data, we obtain the global wellposedness of strong solution with uniform regularity. Moreover, we provide a rigorous justification for the link between the compressible model and the corresponding incompressible model via incompressible limits.
In this paper, we prove the energy conservation for the weak solutions to the three-dimensional equations of compressible magnetohydrodynamic flows (MHD) under certain conditions only about density and velocity. This work is inspired by the seminal work by Yu [27] on the energy conservation of compressible Navier-Stokes equations. Our result indicates that even the magnetic field is taken into account, we only need some regularity conditions of the density and velocity as in [27] to ensure the energy conservation.