14:00 – 15:00 Singular limits of the symmetric hyperbolic equations
Prof. 琚强昌 （北京应用物理与计算数学研究所）
Abstract: The main results of the singular limits of the symmetric hyperbolic equations will be reviewed. Then the recent results of Alven limits for compressible MHD system will be presented.
15:00 – 16:00 On the incompressible fluids with helical symmetry
Abstract: In this talk, we study the weak solutions of the three-dimensional incompressible Euler equations with helical symmetry in the whole space when the helical swirl vanishes. Specifically, we establish the global existence of weak solutions when the initial vorticity lies in L1 ∩ Lp with p > 1. Our result extends the previous work of Bronze, M. Lopes and H. Lopes, where the initial vorticity is compactly supported and belongs to Lp with p >4/3. The key ingredient in this talk involves the explicit analysis of Biot–Savart law with helical symmetry in domain R2 × [−π, π] via the theories of singular integral operators and second order elliptic equations. It is a joint work with Quansen Jiu and Jun Li.
16:00—17:00 Well-posedness and incompressible limit of solutions to compressible Navier-Stokes equations with degenerate viscosity coefficients
Abstract: In this talk, I will first present a recent result on the incompressible limit of compressible Navier-Stokes equations with non-constant viscosity and heat conducting coefficients. The uniform estimates in the Mach number for the strong solutions are derived, provided that the initial density and temperature are close to the constant states. Consequently, the solutions of the compressible Navier-Stokes equations converge to the one of the incompressible Navier-Stokes equations, as the Mach number vanishes. Next, I state another result on the global existence of weak solutions to compressible Navier-Stokes equations with degenerate viscosity.