Small viscosity method and criteria for shock wave existence in relativistic magnetic hydrodynamics

Regularity criteria and uniform estimates for the Boussinesq system with the temperature-dependent viscosity and thermal diffusivity

In this paper we establish some regularity criteria for the 3D Boussinesq system with the temperature-dependent viscosity and thermal diffusivity. We also obtain some uniform estimates for the corresponding 2D case when the fluid viscosity coefficient is a positive constant.

从线性Boltzmann方程与黏性-毛细平衡导出的严格流体动力学

Rigorous Hydrodynamics from Linear Boltzmann Equations and Viscosity-Capillarity Balance

该研究从线性Boltzmann方程出发，利用谱理论与慢流形理论严格推导出流体动力学闭合，并引入熵修正实现纯黏性耗散，以Knudsen最小悖论为例验证了其有效性。

Global existence and semiclassical limit for quantum hydrodynamic equations with viscosity and heat conduction

The hydrodynamic equations with quantum effects are studied in this paper. First we establish the global existence of smooth solutions with small initial data and then in the second part, we establish the convergence of the solutions of the quantum hydrodynamic equations to those of the classical hydrodynamic equations. The energy equation is considered in this paper, which added new difficulties to the energy estimates, especially to the selection of the appropriate Sobolev spaces.

Global Regularity for A Radiation Hydrodynamics Model with Viscosity and Thermal Conductivity

In this paper, we study the global wellposedness of a radiation hydrodynamics model with viscosity and thermal conductivity. It is now well-understood that, unlike the compressible Euler equations whose smooth solutions must blow up in finite time no matter how small and how smooth the initial data is, the dissipative structure of such a radiation hydrodynamics model can indeed guarantee that its one-dimensional Cauchy problem admits a unique global smooth solution provided that the initial data is sufficiently small, while for large initial data, even if the heat conductivity is taken into ac…