Global well-posedness of a Prandtl model from MHD in Gevrey function spaces

Almost global well-posedness of Kirchhoff equation with Gevrey data

Article history: Received 26 November 2016 Accepted after revision 3 April 2017 Available online 18 April 2017 Presented by the Editorial Board The aim of this note is to present the almost global well-posedness result for the Cauchy problem for the Kirchhoff equation with large data in Gevrey spaces. We also briefly discuss the corresponding results in bounded and in exterior domains. © 2017 A...

On well-posedness of the Cauchy problem for MHD system in Besov spaces

This paper studies the global well-posedness of solutions to the Cauchy problem of incompressible magneto-hydrodynamics system for large initial data in homogeneous Besov space Ḃ 2 p −1 p,r (R) for 2 < p < ∞ and 1 ≤ r < ∞. In the case of spatial dimension n ≥ 3 we establish the global well-posedness of solution for small data and the local one for large data in Besov space Ḃ n p −1 p,r (R), 1 ≤...

Global Well-Posedness for a Family of MHD-Alpha-Like Models

On the well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces

In this paper, we prove the local well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces and obtain blow-up criterion of smooth solutions. Specially, a recovered proof of [7] for the incompressible Euler equation is given.

Well-posedness of the Infinite Prandtl Number Model for Convection with Temperature-Dependent Viscosity

We establish the well-posedness of the infinite Prandtl number model for convection with temperature-dependent viscosity, free-slip boundary condition and zero horizontal fluxes.