The Euler equations in planar nonsmooth convex domains
@article{Bardos2013TheEE, title={The Euler equations in planar nonsmooth convex domains}, author={Claude W. Bardos and Francesco Di Plinio and Roger Temam}, journal={Journal of Mathematical Analysis and Applications}, year={2013}, volume={407}, pages={69-89} }
18 Citations
Uniqueness for the 2-D Euler equations on domains with corners
- Mathematics
- 2013
For a large class of non smooth bounded domains, existence of a global weak solution of the 2D Euler equations, with bounded vorticity, was established by G\'erard-Varet and Lacave. In the case of…
Uniqueness for Two-Dimensional Incompressible Ideal Flow on Singular Domains
- MathematicsSIAM J. Math. Anal.
- 2015
We prove uniqueness of the weak solution of the Euler equations for compactly supported, single signed, and bounded initial vorticity in simply connected planar domains with corners forming angles…
Euler Equations on General Planar Domains
- Mathematics, Computer ScienceAnnals of PDE
- 2021
We obtain a general sufficient condition on the geometry of possibly singular planar domains that guarantees global uniqueness for any weak solution to the Euler equations on them whose vorticity is…
MODELING THE LID DRIVEN FLOW : THEORY AND COMPUTATION
- Mathematics
- 2017
Abstract. Motivated by the study of the corner singularities in the so-called cavity flow, we establish in the first part of this article, the existence and uniqueness of solutions in L(Ω) for the…
The Euler Equations in Planar Domains with Corners
- MathematicsArchive for Rational Mechanics and Analysis
- 2019
When the velocity field is not a priori known to be globally almost Lipschitz, global uniqueness of solutions to the two-dimensional Euler equations has been established only in some special cases,…
Uniqueness of the 2D Euler equation on a corner domain with non-constant vorticity around the corner
- Mathematics
- 2020
We consider the 2D incompressible Euler equation on a corner domain $\Omega$ with angle $\nu\pi$ with $\frac{1}{2}<\nu<1$. We prove that if the initial vorticity $\omega_0 \in L^{1}(\Omega)\cap…
Very weak solutions of the Stokes problem in a convex polygon
- Mathematics
- 2015
Motivated by the study of the corner singularities in the so-called cavity flow, we establish in this article, the existence and uniqueness of solutions in $L^2(\Omega)^2$ for the Stokes problem in a…
Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion
- MathematicsPhysica D: Nonlinear Phenomena
- 2018
The Two Dimensional Euler Equations on Singular Exterior Domains
- Mathematics
- 2015
This paper is a follow-up of Gérard-Varet and Lacave (Arch Ration Mech Anal 209(1):131–170, 2013), on the existence of global weak solutions to the two dimensional Euler equations in singular…
The 2D Euler–Boussinesq Equations in Planar Polygonal Domains with Yudovich’s Type Data
- Mathematics
- 2014
We address the well-posedness of the 2D (Euler)–Boussinesq equations with zero viscosity and positive diffusivity in the polygonal-like domains with Yudovich’s type data, which gives a positive…
References
SHOWING 1-10 OF 59 REFERENCES
Uniqueness Theorem for the Basic Nonstationary Problem in the Dynamics of an Ideal Incompressible Fluid
- Mathematics
- 1995
A bstract . The initial boundary value problem is considered for the Euler equations for an incompressible fluid in a bounded domain D ⊂ Rn. It is known [Y1] that uniqueness holds for those flows…
Uniqueness for Two-Dimensional Incompressible Ideal Flow on Singular Domains
- MathematicsSIAM J. Math. Anal.
- 2015
We prove uniqueness of the weak solution of the Euler equations for compactly supported, single signed, and bounded initial vorticity in simply connected planar domains with corners forming angles…
The 2D Euler equation on singular domains
- Mathematics
- 2011
We establish the existence of global weak solutions of the 2D incompressible Euler equation, for a large class of non-smooth open sets. These open sets are the complements (in a simply connected…
Asymptotic analysis of the Stokes problem on general bounded domains: the case of a characteristic boundary
- Mathematics
- 2010
The goal of this article is to study the asymptotic behaviour of the solutions of linearized Navier–Stokes equations (LNSE), when the viscosity is small, in a general (curved) bounded and smooth…
Incompressible Fluid Flows on Rough Domains
- Mathematics
- 2000
There is a substantial literature on the existence of solutions to the Euler and Navier-Stokes equations for incompressible flows in bounded domains Most papers concentrate on the case of domains…
Boundary Layers on Sobolev–Besov Spaces and Poisson's Equation for the Laplacian in Lipschitz Domains
- Mathematics
- 1998
We study inhomogeneous boundary value problems for the Laplacian in arbitrary Lipschitz domains with data in Sobolev–Besov spaces. As such, this is a natural continuation of work in [Jerison and…
Vorticity and incompressible flow
- Mathematics
- 2001
Preface 1. An introduction to vortex dynamics for incompressible fluid flows 2. The vorticity-stream formulation of the Euler and the Navier-Stokes equations 3. Energy methods for the Euler and the…
Weak Solutions with Decreasing Energy¶of Incompressible Euler Equations
- Mathematics
- 2000
Abstract: Weak solution of the Euler equations is an L2-vector field u(x, t), satisfying certain integral relations, which express incompressibility and the momentum balance. Our conjecture is that…
On the Cauchy problem for Boltzmann equations: global existence and weak stability
- Mathematics
- 1989
We study the large-data Cauchy problem for Boltzmann equations with general collision kernels. We prove that sequences of solutions which satisfy only the physically natural a priori bounds converge…