题目：Striated Regualrity of 2-D Inhomogeneous Incompressible Navier-Stokes System with Variable Viscosity
报告人：张平 研究员 （中科院 数学与系统科学研究院）
摘要：In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous across some smooth interface. Compared with the previous results for the inhomogeneous Navier-Stokes equations with constant viscosity, the main difficulty here lies in the fact that the L^1 in time Lipschitz estimate of the velocity field can not be obtained by energy method. Motivated by the key idea of Chemin to solve 2-D vortex patch of ideal fluid, namely, striated regularity can help to get the L^\infty boundedness of the double Riesz transform, we derive the a priori L^1 in time Lipschitz estimate of the velocity field under the assumption that the viscous coefficient is close enough to a positive constant in the bounded function space. As an application, we shall prove the propagation of H^3 regularity of the interface between fluids with different densities.
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