A global existence result in Sobolev spaces for MHD system in the half-plane

Emanuela Casella; Paola Trebeschi

Displaying similar documents to “A global existence result in Sobolev spaces for MHD system in the half-plane”

Global solutions of the Cauchy problem for a viscous polytropic ideal gas

Song Jiang (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On global motion of a compressible barotropic viscous fluid with boundary slip condition

Takayuki Kobayashi, Wojciech Zajączkowski (1999)

Applicationes Mathematicae

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Global-in-time existence of solutions for equations of viscous compressible barotropic fluid in a bounded domain Ω ⊂ $ℝ^{3}$ with the boundary slip condition is proved. The solution is close to an equilibrium solution. The proof is based on the energy method. Moreover, in the $L_{2}$ -approach the result is sharp (the regularity of the solution cannot be decreased) because the velocity belongs to $H^{2 + α, 1 + α / 2} (Ω \times ℝ_{+})$ and the density belongs to $H^{1 + α, 1 / 2 + α / 2} (Ω \times ℝ_{+})$ , α ∈ (1/2,1).

Boundary-value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow

H. Beirão da Veiga (1988)

Rendiconti del Seminario Matematico della Università di Padova

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On the Euler equations of incompressible perfect fluids

R. Temam (1974-1975)

Séminaire Équations aux dérivées partielles (Polytechnique)

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On nonstationary motion of a fixed mass of a viscous compressible barotropic fluid bounded by a free boundary

Ewa Zadrzyńska, Wojciech Zajączkowski (1999)

Colloquium Mathematicae

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A property of multiplication in Sobolev spaces. Some applications

Tullio Valent (1985)

Rendiconti del Seminario Matematico della Università di Padova

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Study of Anisotropic MHD system in Anisotropic Sobolev spaces

Jamel Ben Ameur, Ridha Selmi (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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Three-dimensional anisotropic magneto-hydrodynamical system is investigated in the whole space $ℝ^{3}$ . Existence and uniqueness results are proved in the anisotropic Sobolev space $H^{0, s}$ for $s > 1 / 2$ . Asymptotic behavior of the solution when the Rossby number goes to zero is studied. The proofs, where the incompressibility condition is crucial, use the energy method, an appropriate dyadic decomposition of the frequency space, product laws in anisotropic Sobolev spaces and Strichartz-type estimates. ...