Displaying similar documents to “The unstable spectrum of the Navier–Stokes operator in the limit of vanishing viscosity”

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.

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...

Global regularity for the 3D inhomogeneous incompressible Navier-Stokes equations with damping

Kwang-Ok Li, Yong-Ho Kim (2023)

Applications of Mathematics

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This paper is concerned with the 3D inhomogeneous incompressible Navier-Stokes equations with damping. We find a range of parameters to guarantee the existence of global strong solutions of the Cauchy problem for large initial velocity and external force as well as prove the uniqueness of the strong solutions. This is an extension of the theorem for the existence and uniqueness of the 3D incompressible Navier-Stokes equations with damping to inhomogeneous viscous incompressible fluids. ...