Optimal convergence rates for three-dimensional turbulent flow equations

In this paper,the convergence rates of solutions to the three-dimensional turbulent flow equations are considered.By combining the Lp-Lq estimate for the linearized equations and an elaborate energy method,the convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the equilibrium state is small in the H3-framework.More precisely,the optimal convergence rates of the solutions and their first-order derivatives in the L2-norm are obtained when the Lp-norm of the perturbation is bounded for some p ∈[1,6/5).     

WELL-POSEDNESS IN CRITICAL SPACES FOR THE FULL COMPRESSIBLE MHD EQUATIONS

In this paper we prove local well-posedness in critical Besov spaces for the full compressible MHD equations in R^N, N≥ 2, under the assumptions that the initialdensity is bounded away from zero. The proof relies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.     

可压缩磁流体方程光滑解的爆破性

在初始密度和磁通量具有紧支集的条件下,该文证明高维可压缩磁流体方程柯西问题光滑解的爆破现象.其中磁流体方程的黏性系数,热传导系数以及磁扩散系数都是依赖于密度和温度的.