Kengo NAKAI 博士:Mathematical and numerical analysis of the energy cascade, and regularity of vorticity for the Navier-Stokes Equations with general viscosity

讲座时间 Datetime: 
星期二, 2017/11/28 - 15:0016:30
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报告摘要 Abstract: 

   We talk two topics. First of all, our purpose is to clarify the energy cascade mechanism  for the incompressible Navier–Stokes equations. For the first step, we study the 3D NS equations with partial hyperviscosity (dissipation is removed from some of the low Fourier modes) with Direct Numerical Simulation. This study direction is highly related to the previous result by T. Elgindi, W. Hu, V. Šverák (2017). This is a joint work with Professors Kishimoto, Saiki and Yoneda.
   On the other hand, we give a refined blow-up criterion for solutions of the 3D NS equations with fractional Laplacian. The criterion is composed by the direction field of the vorticity and its magnitude simultaneously.  Our result is an improvement of previous results Y. Zhou (2005), and D. Chae (2007).