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2010年07月22日

【期刊论文】Global Well-Posedness for Compressible Navier-Stokes Equations with Highly Oscillating Initial Velocity

Changxing Miao, Qionglei Chen, Zhifei Zhang

Communications on Pure and Applied Mathematics,2010,LXIII,(1):1173–1224

2010年05月10日

摘要

In this paper, we prove global well-posedness for compressible Navier-Stokesequations in the critical functional framework with the initial data close to astable equilibrium. This result allows us to construct global solutions for thehighly oscillating initial velocity. The proof relies on a new estimate for thehyperbolic/parabolic system with convection terms.

关键词: Global well-posedness,, Compressible Navier-Stokes equations,, Highly oscillating

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2010年07月22日

【期刊论文】On the well-posedness of the ideal MHD equations in the Triebel-Lizorkin spaces

Qionglei Chen, Changxing Miao , Zhifei Zhang

Arch. Rational Mech. Anal. ,2010,195(1):)561-5

2010年10月01日

摘要

In this paper, we prove the local well-posedness for the ideal MHD equations in the Triebel–Lizorkin spaces and obtain a blow-up criterion of smooth solutions. Specifically, we fill a gap in a step of the proof of the local well-posedness part for the incompressible Euler equation in Chae (Comm Pure Appl Math 55:654–678: 2002).

关键词: Triebel–Lizorkin spaces,, particle trajectory mapping,, Lagrangian coordinates

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