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第24期学术报告: New properties of global weak solutions of n-dimensional Navier-Stokes equations

时间:2019-06-11 14:58:08  作者:  点击: 107 次

24期学术报告

题 目New properties of global weak solutions of n-dimensional Navier-Stokes equations

时  间2019年6月21日16:00-17:00

地  点8号楼425

报告人张领海

    张领海,教授,博士生导师。主要从事偏微分方程组的稳定性和衰减率等领域的研究工作。

摘要:Consider the standard n-dimensional incomprehensible Navier-Stokes equations and the linear heat equation. Here are several very interesting questions. Can we establish better decay estimates with sharp rates? Can we accomplish the exact limits of the weak solutions and of all order derivatives, as time approaches infinity, in terms of the diffusion coefficient, the spatial dimension, the order of the derivative, the integrals of functions related to the initial function, the integrals of functions related to the external force as well as the integrals of the nonlinear functions $u_iu_j$? Can we use the solution of the heat equation to appropriate the solutions of the Navier-Stokes equations? Will the exact limits of the solutions of the Navier-Stokes equations and the exact limits of the solution of the heat equation increase at the same rate as the order of the derivative increases? If we drop the nonlinear terms in the Navier-Stokes equations, will the exact limits of the solutions of the Navier-Stokes equations reduce to the exact limits of the solution of the heat equation?I will give positive solutions to all of these problems in this talk.

 

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