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

Song Jiang

Displaying similar documents to “Global solutions of the Cauchy problem for a viscous polytropic ideal gas”

On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion

Piotr Mucha, Wojciech Zajączkowski (2000)

Applicationes Mathematicae

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The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that $u \in W_{r}^{2, 1} ({\tilde{Ω}}^{T})$ with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the $L_{p}$ -approach the Lagrangian coordinates must be used....

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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Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method

Alberto Valli (1983)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Low Mach number limit for viscous compressible flows

Raphaël Danchin (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this survey paper, we are concerned with the zero Mach number limit for compressible viscous flows. For the sake of (mathematical) simplicity, we restrict ourselves to the case of barotropic fluids and we assume that the flow evolves in the whole space or satisfies periodic boundary conditions. We focus on the case of ill-prepared data. Hence highly oscillating acoustic waves are likely to propagate through the fluid. We nevertheless state the convergence to the incompressible Navier-Stokes...

Existence of a global solution to a model problem of atmosphere dynamics.

Gatapov, B.V., Kazhikhov, A.V. (2005)

Sibirskij Matematicheskij Zhurnal

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On the stationary motion of compressible viscous fluids

Paolo Secchi (1994)

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).