偏微分方程研讨班

报告人：陶 涛（山东大学数学系 ）

题  目：H？lder continuous weak solution of Boussinesq equations(I), (II)

时  间：2018.07.26（星期四），14 :30-16:30
        2018.08.02（星期四），14 :30-16:30

地  点：数学院南楼N208室

摘 要： Recent year, Camillo De Lellis and La ？szlo ？ Sze ？kelyhidi make an important breakthrough on the construction of Ho ？lder continuous weak solution for the incompressible Euler equations by introducing an iterative scheme(convex integration). Finally, Philip Isett give a proof of Onsager conjecture by combining this iterative scheme and a new “gluing approximation” technique. Inspired by their work, we consider the related problem of Boussinesq equations and also construct Ho ？lder continuous weak solution by improving the iterative scheme.
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报告人：陶 涛（山东大学数学系 ）

题  目：Zero-viscosity limit of Navier-Stokes equations with Navier-slip boundary condition

时  间：2018.08.09（星期四），14 :30-16:30

地  点：数学院南楼N208室

摘  要：In this talk, we discuss the zero-viscosity limit problem of the Navier-Stokes equations in the half space with the Navier friction boundary condition where the slip length is a power of the viscosity: u^ε-ε^γ 〖？u/？y〗^ε|_{y=0}=0. We rigorously justify the convergence process in L^∞  sense from Navier-Stokes equations to Euler equations and some Prandtl equations for Gervey data when γ ∈[0,1] and is a rational number.