On the global well-posedness of the Boussinesq system with zero viscosity

Taoufik Hmidi

Displaying similar documents to “On the global well-posedness of the Boussinesq system with zero viscosity”

A note on the relaxation-time limit of the isothermal Euler equations.

Xu, Jiang, Fang, Daoyuan (2007)

Boundary Value Problems [electronic only]

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Asymptotic stability of Oseen vortices for a density-dependent incompressible viscous fluid

L. Miguel Rodrigues (2009)

Annales de l'I.H.P. Analyse non linéaire

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A regularity criterion for the dissipative quasi-geostrophic equations

Hongjie Dong, Nataša Pavlović (2009)

Annales de l'I.H.P. Analyse non linéaire

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On non-homogeneous viscous incompressible fluids. Existence of regular solutions

Jérôme Lemoine (1997)

Commentationes Mathematicae Universitatis Carolinae

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We consider the flow of a non-homogeneous viscous incompressible fluid which is known at an initial time. Our purpose is to prove that, when $Ω$ is smooth enough, there exists a local strong regular solution (which is global for small regular data).

On the hierarchies of higher order mKdV and KdV equations

Axel Grünrock (2010)

Open Mathematics

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The Cauchy problem for the higher order equations in the mKdV hierarchy is investigated with data in the spaces ${\hat{H}}_{s}^{r} (ℝ)$ defined by the norm ${∥v_{0}∥}_{{\hat{H}}_{s}^{r} (ℝ)} : = {∥{〈ξ〉}^{s} \hat{v_{0}}∥}_{L_{ξ}^{r^{'}}}, 〈ξ〉 = {(1 + ξ^{2})}^{\frac{1}{2}}, \frac{1}{r} + \frac{1}{r^{'}} = 1$ . Local well-posedness for the jth equation is shown in the parameter range 2 ≥ 1, r > 1, s ≥ $\frac{2 j - 1}{2 r^{'}}$ . The proof uses an appropriate variant of the Fourier restriction norm method. A counterexample is discussed to show that the Cauchy problem for equations of this type is in general ill-posed in the C 0-uniform sense, if s < $\frac{2 j - 1}{2 r^{'}}$ . The results for r =...