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Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations
In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove theExpand
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Spectral instability of characteristic boundary layer flows
In this paper, we construct growing modes of the linearized Navier-Stokes equations about generic stationary shear flows of the boundary layer type in a regime of sufficiently large Reynolds number:Expand
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Topography Influence on the Lake Equations in Bounded Domains
We investigate the influence of the topography on the lake equations which describe the two-dimensional horizontal velocity of a three-dimensional incompressible flow. We show that the lake equationsExpand
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Global existence for a class of triangular parabolic systems on domains of arbitrary dimension
A class of triangular parabolic systems given on bounded domains of R n with arbitrary n is investigated. Sufficient conditions on the structure of the systems are found to assure that weak solutionsExpand
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SHIGESADA-KAWASAKI-TERAMOTO MODEL ON HIGHER DIMENSIONAL DOMAINS
We investigate the existence of a global attractor for a class of triangular cross diusion systems in domains of any dimension. These sys- tems includes the Shigesada-Kawasaki-Teramoto (SKT) model,Expand
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Spectral stability of Prandtl boundary layers: An overview
Abstract In this paper we show how the stability of Prandtl boundary layers is linked to the stability of shear flows in the incompressible Navier–Stokes equations. We then recall classical physicalExpand
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Linear Stability Analysis of a Hot Plasma in a Solid Torus
This paper is a first step toward understanding the effect of toroidal geometry on the rigorous stability theory of plasmas. We consider a collisionless plasma inside a torus, modeled by theExpand
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L∞ instability of Prandtl layers
In 1904, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of incompressible Navier Stokes equations near a boundary as the viscosity goes to 0. His AnsatzExpand
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Remarks on the inviscid limit for the compressible flows
We establish various criteria, which are known in the incompressible case, for the validity of the inviscid limit for the compressible Navier-Stokes flows considered in a general domain $\Omega$ inExpand
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Sharp bounds on linear semigroup of Navier Stokes with boundary layer norms
In this paper, we derive sharp bounds on the semigroup of the linearized Navier-Stokes equations near a stationary boundary layer on the half space. The bounds are obtained uniformly in the inviscidExpand
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