报告人：王勇 副研究员（中国科学院应用数学所）

报告题目: Diffusive wave in the low Mach limit for compressible Navier–Stokes equations

报告摘要: The low Mach limit for 1D non-isentropic compressible Navier-Stokes flow, whose density and temperature have different asymptotic states at infinity, is rigorously justified. The problems are considered on both well-prepared and ill-prepared data. For the well-prepared data, the solutions of compressible Navier-Stokes equations are shown to converge to a nonlinear diffusion wave solution globally in time as Mach number goes to zero when the difference between the states at $\pm\infty$ is suitably small. In particular, the velocity of diffusion wave is only driven by the variation of temperature. It is further shown that the solution of compressible Navier-Stokes system also has the same property when Mach number is small, which has never been observed before. The convergence rates on both Mach number and time are also obtained for the well-prepared data. For the ill-prepared data, the limit relies on the uniform estimates including  weighted time derivatives and an extended convergence lemma. And the difference between the states at $\pm\infty$ can be arbitrary large in this case.

报告人简介：王勇，中科院数学与系统科学研究院副研究员，于2012年在中国科学院数学与系统科学研究院获得理学博士学位。毕业后赴香港中文大学进行博士后研究，并于2014回到中国科学院数学与系统科学研究院工作，现任助理研究员，从事非线性偏微分方程的研究,在Advance in Math., ARMA, CMP和SIAM-MAJ 等国际重要数学杂志发表论文10余篇.

报告时间：2019年5月16日（星期四）上午9：00

报告地点：科技楼南楼702