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Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations

- Daniel Han-Kwan, T. Nguyen
- Physics, Mathematics
- 7 July 2015

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 the… Expand

21 6- PDF

Spectral instability of characteristic boundary layer flows

- E. Grenier, Y. Guo, T. Nguyen
- Mathematics, Physics
- 15 June 2014

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

71 5- PDF

Topography Influence on the Lake Equations in Bounded Domains

- C. Lacave, T. Nguyen, B. Pausader
- Mathematics, Physics
- 10 June 2013

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 equations… Expand

8 4- PDF

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 solutions… Expand

28 2- PDF

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

53 1- PDF

Spectral stability of Prandtl boundary layers: An overview

- E. Grenier, Y. Guo, T. Nguyen
- Physics, Mathematics
- 17 June 2014

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 physical… Expand

52 1- PDF

Linear Stability Analysis of a Hot Plasma in a Solid Torus

- T. Nguyen, W. Strauss
- Physics, Mathematics
- 6 August 2013

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 the… Expand

10 1- PDF

L∞ instability of Prandtl layers

- E. Grenier, T. Nguyen
- 2019

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 Ansatz… Expand

21 1- PDF

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 $\Omega$ in… Expand

8 1- PDF

Sharp bounds on linear semigroup of Navier Stokes with boundary layer norms

- E. Grenier, T. Nguyen
- Mathematics
- 2 March 2017

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 inviscid… Expand

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