91直播

报告人: 张剑文 (厦门大学)

时  间: 2018年5月26日  上午8：30--9：20

地  点: 理科楼LA106

摘  要:This talk is concerned with the Cauchy problem of the three-dimensional compressible Navier-Stokes equations with vacuum and external potential forces which could be arbitrarily large. The global well-posedness of strong solution with large oscillations and vacuum is proved, provided the initial data is of small energy and the unique steady state is strictly away from vacuum. It is worth mentioning that although the strong solution may contain vacuum states, we only require that the initial momentum $m_0$ equals to $\rho_0u_0$ (i.e., $m_0=\rho_0u_0$), which is indeed a weaker compatibility condition than the one in the previous literature. It is also shown that if the initial data $(\rho_0,u_0)$ are more regular and satisfy the compatibility condition used for the existence of strong solutions in the previous works, then the strong solution is indeed a classical one away from the initial time. The global existence of weak solutions for the case of discontinuous initial data containing vacuum. The large-time behavior of the solution is studied.

报告人简介:张剑文，厦门大学数学科学91直播 教授、博士生导师，主要研究方向为流体力学中的偏微分方程（组），在SIAM J. Math. Anal., JDE, M3AS, Nonlinearity等期刊发表论文三十余篇，连续主持多项国家自然科学基金。

91直播 联系人: 穆春来

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