Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics

DOI10.1090/S0002-9939-2012-11591-6zbMath1283.35080arXiv1201.6326OpenAlexW2093110305MaRDI QIDQ2838956

Raphaël Danchin

Publication date: 4 July 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.6326

zbMATH Keywords

incompressible Euler equationsinviscid Boussinesq system

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Stratification effects in inviscid fluids (76B70) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31)

Related Items (29)

On the global regularity of the 2D Boussinesq equations with fractional dissipation ⋮ On the two-dimensional Boussinesq equations with temperature-dependent thermal and viscosity diffusions in general Sobolev spaces ⋮ Global existence and uniqueness of solutions to the three-dimensional Boussinesq equations ⋮ Global regularity results of the 2D Boussinesq equations with fractional Laplacian dissipation ⋮ On certain commutator estimates for vector fields ⋮ Finite-time singularity formation for strong solutions to the Boussinesq system ⋮ An improved regularity criterion for the 2D inviscid Boussinesq equations ⋮ Global regularity results for the 2D Boussinesq equations with partial dissipation ⋮ Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain ⋮ Regularity criterion for the 2D inviscid Boussinesq equations ⋮ On the regularity of solutions to the 2D Boussinesq equations satisfying type I conditions ⋮ Global Sobolev regular solution for Boussinesq system ⋮ Yudovich type solution for the 2D inviscid Boussinesq system with critical and supercritical dissipation ⋮ Small global solutions to the damped two-dimensional Boussinesq equations ⋮ Long time solutions for the 2D inviscid Boussinesq equations with strong stratification ⋮ Strongly stratified limit for the 3D inviscid Boussinesq equations ⋮ Remarks on global regularity of the 2D Boussinesq equations with fractional dissipation ⋮ On the existence of long-time classical solutions for the 2D inviscid Boussinesq equations ⋮ Remarks on the improved regularity criterion for the 2D Euler-Boussinesq equations with supercritical dissipation ⋮ A global regularity result for the 2D Boussinesq equations with critical dissipation ⋮ Global smooth solutions to the \(n\)-dimensional damped models of incompressible fluid mechanics with small initial datum ⋮ On the regularity criterion for the 2D Boussinesq equations involving the temperature ⋮ Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation ⋮ Blow-up criterion of smooth solutions for the Boussinesq equations ⋮ Global smooth solution to the 2D Boussinesq equations with fractional dissipation ⋮ Relaxation of the Boussinesq system and applications to the Rayleigh-Taylor instability ⋮ Removing type II singularities off the axis for the three dimensional axisymmetric Euler equations ⋮ The lifespan of solutions to the inviscid 3D Boussinesq system ⋮ Stratified Boussinesq equations with a velocity damping term

Cites Work

• Unnamed Item
• Unnamed Item
• The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces
• Incompressible viscous flows in borderline Besov spaces
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• The existence and uniqueness of nonstationary ideal incompressible flow in exterior domains in \(R^ 3\)
• Hydrodynamics in Besov spaces
• Precise regularity results for the Euler equations.
• Local well-posedness for the incompressible Euler equations in the critical Besov spaces.
• Global existence for two-dimensional incompressible Euler system in \(B_{\infty,1}^1\).
• Vorticity and Incompressible Flow
• Fourier Analysis and Nonlinear Partial Differential Equations
• Existence of Solution for the Euler Equations in a Critical Besov Space (ℝⁿ)
• Axisymmetric incompressible flows with bounded vorticity
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
• On besov - hardy - sobolev spaces in domains and regular elliptic boundary value problems. the case
• Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations
• Small-scale structures in Boussinesq convection
• The Euler equation in an exterior domain. Local existence and appearance of singularities
• Local well-posedness and blowup criterion of the Boussinesq equations in critical Besov spaces

This page was built for publication: Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics