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2010年07月22日

【期刊论文】A losing estimates for the ideal MHD equations with application to blow-up critersion

Marco Cannone, Qionglei Chen, Changxing Miao

SIAM J. Math. Anal.,2007,38(6):1847–1859

2007年03月05日

摘要

In this paper we study the blow-up criterion of smooth solution to the ideal MHDequations in Rn. By means of the Fourier frequency localization and Bony paraproduct decomposition,we show a losing estimate for the ideal MHD equations and apply it to establish an improvedblow-up criterion of smooth solutions. As a special case, we recover a previous result of Planchonfor the incompressible Euler equations.

关键词: ideal MHD equations,, blow-up,, Littlewood-Paley decomposition,, Besov space, ideal MHD equations,, blow-up,, Littlewood-Paley decomposition,, Besov space

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2010年07月22日

【期刊论文】A New Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation

Qionglei Chen, Changxing Miao, Zhifei Zhang

Commun. Math. Phys. ,2007,271(1): 821-838

2007年02月15日

摘要

We show a new Bernstein's inequality which generalizes the results ofCannone-Planchon, Danchin and Lemarié-Rieusset. As an application of this inequality,we prove the global well-posedness of the 2D quasi-geostrophic equation with thecritical and super-critical dissipation for the small initial data in the critical Besov space,and local well-posedness for the large initial data.

关键词: New Bernstein inequality,, Littlewood-Paley Decomposition

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2010年07月22日

【期刊论文】The Beale-Kato-Majda criterion for the 3D magneto-hydrodynamics equations

Qionglei Chen, Changxing Miao, Zhifei Zhang

Commun. Math. Phys. ,2007,275(1):861-872

2007年05月15日

摘要

Abstract: We study the blow-up criterion of smooth solutions to the 3D MHD equations.By means of the Littlewood-Paley decomposition, we prove a Beale-Kato-Majda type blow-up criterion of smooth solutions via the vorticity of velocity only, namelysupj∈Z_T0__j (∇×u)_∞dt, where_j is the frequency localization operator in the Littlewood-Paley decomposition

关键词: Frequency localization operator,, Littlewood-Paley decomposition,, Besov space,, MHD

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