Displaying similar documents to “Global existence for a one-dimensional model in gas dynamics”

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...

The resolution of the Navier-Stokes equations in anisotropic spaces.

Dragos Iftimie (1999)

Revista Matemática Iberoamericana

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In this paper we prove global existence and uniqueness for solutions of the 3-dimensional Navier-Stokes equations with small initial data in spaces which are H in the i-th direction, δ + δ + δ = 1/2, -1/2 < δ < 1/2 and in a space which is L in the first two directions and B in the third direction, where H and B denote the usual homogeneous Sobolev and Besov spaces.

Well-posedness of the Euler and Navier-Stokes equations in the Lebesque spaces L (R).

Tosio Kato, Gustavo Ponce (1986)

Revista Matemática Iberoamericana

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In this paper we show that the Euler equation for incompressible fluids in R2 is well posed in the (vector-valued) Lebesgue spaces Ls p = (1 - ∆)-s/2 Lp(R2) with s > 1 + 2/p, 1 < p < ∞ and that the same is true of the Navier-Stokes equation uniformly in the viscosity ν.