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数学学院、所系列学术报告(737场):西北大学李振邦博士

发表于: 2017-09-25 09:39  点击:

  目 :Global well- posedness of the 2-D incompressible Navier-Stokes-Cahn-Hilliard system with a singular free energy density 

报告人:西北大学  李振邦 博士

  间:2017930日 上午9:00-10:00

  点:数学楼第一报告厅

 

  要:We prove the global well-posedness of the 2-D incompressible Navier-stokes/Cahn-Hilliard system with a logarithmic free energy. The model is a so-called diffuse interface model, which is capable of describing the evolution of droplet formation and collision during flow. Due to lack of a maximum principle for four-order parabolic equations. It is hard to separate the solutions from the singular values of the potential, which allow us to reduce the problem to one with a regular potential. By comparison principle for an approximate second parabolic equation, we are able to separate the solutions away the singular points of the CH equation. And then, the singular problem is reduced to a regular problem. Therefor, by some energy estimates and bootstrap argument, our main result is proved.