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2014年07月07日

【期刊论文】On the global well-posedness for the Boussinesq system with horizontal dissipation

hangxing Miao, Xiaoxin Zheng

Commun. Math. Phys.,2013,321(1):33–67

2013年09月10日

摘要

In this paper, we investigate the Cauchy problem for the tridimensional Boussinesq equations with horizontal dissipation. Under the assumption that the initial data is axisymmetric without swirl, we prove the global well-posedness for this system. In the absence of vertical dissipation, there is no smoothing effect on the vertical derivatives. To make up this shortcoming, we first establish a magic relationship between $\\frac{u^{r}}{r}$ and $\\frac{\\omega_\\theta}{r}$ by taking full advantage of the structure of the axisymmetric fluid without swirl and some tricks in harmonic analysis. This together with the structure of the coupling of \\eqref{eq1.1} entails the desired regularity.

关键词: Boussinesq system,, losing estimate,, horizontal dissipation,, anisotropic inequality,, global well-posedness.,

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2014年07月07日

【期刊论文】Global regularity for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing

Marco Cannone, Changxing Miao, Liutang Xue

Proc. London Math. Soc.,2013,106(3): 650–674

2013年05月05日

摘要

We consider the 2D quasi-geostrophic equation with supercritical dissipation and dispersive forcing in the whole space.When the dispersive amplitude parameter is large enough, we prove the global well-posedness of strong solution to the equation with large initial data. We also show the strong convergence result as the amplitude parameter goes to $\\infty$. Both results rely on the Strichartz-type estimates for the corresponding linear equation.

关键词: upercritical quasi-geostrophic equation,, dispersive effect,, Strichartz-type estimate,, global well-posedness.,

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2019年05月20日

【期刊论文】Geometric,topological and differentiable rigidity of submanifolds in space forms

H. W. Xu, J. R. Gu

Geom. Funct. Anal.,2013,23(1):1684-1703

2013年06月20日

摘要

In this paper, the authors investigate rigidity of geometric, topological and differentiable structures of compact submanifolds in a space form.

关键词: Submanifolds,, rigidity and sphere theorems,, Ricci curvature,, Ricci flow,, stable currents

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