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2010年07月22日

【期刊论文】On convergence of solutions of fractal Burgers equation toward rarefaction waves

Grzegorz Karch, Changxing Miao, Xiaojing Xu

SIAM J. Math. Anal,2008,39(5):1536-1549

2008年09月10日

摘要

In this paper, the large time behavior of solutions of the Cauchy problem for the one-dimensional fractal Burgers equation with α ∈ (1, 2) is studied. It is shown that if the nondecreasing initial datum approaches the constant states u± (u− < u+) as x → ±∞, respectively, then the corresponding solution converges toward the rarefaction wave, i.e., the unique entropy solution of the Riemann problem for the nonviscous Burgers equation.

关键词: Fractal Burgers equation,, asymptotic behavior,, rarefaction wave,, Riemann problem,, Levy process

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2010年07月22日

【期刊论文】On the well-posedness for the viscous shallow water equations

Qionglei Chen, Changxing Miao, Zhifei Zhang

SIAM J. MathH. Anal. ,2008,20(2):443–474

2008年03月10日

摘要

In this paper, we prove the existence and uniqueness of the solutions for the twodimensional viscous shallow water equations with low regularity assumptions on the initial data as well as the initial height bounded away from zero.

关键词: Shallow water equations,, well-posedness,, Bony', s paraproduct decomposition,, weight Besov space

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2010年07月22日

【期刊论文】On the regularity criterion of weak solution for the 3D viscous magneto-hydrodynamics equations

Qionglei Chen, Changxing Miao, Zhifei Zhang

Commun. Math. Phys. ,2008,284(1): 919-930

2008年02月20日

摘要

We improve and extend some known regularity criterion of the weak solution for the 3D viscous Magneto-hydrodynamics equations by means of the Fourier localization technique and Bony's para-product decomposition.

关键词: Bony', s para-product decomposition,, Fourier localization technique,, regularity criterion

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