Global regularity results of the 2D Boussinesq equations with fractional Laplacian dissipation

DOI10.1007/s00021-015-0245-2zbMath1346.35168arXiv1506.00470OpenAlexW3100241898MaRDI QIDQ2629306

Zhuan Ye, Xiaojing Xu

Publication date: 6 July 2016

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.00470

zbMATH Keywords

Besov spaceglobal regularity2D Boussinesq equationsfractional Laplacian dissipation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Maximal functions, Littlewood-Paley theory (42B25) Fractional derivatives and integrals (26A33) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (5)

A priori estimates for free boundary problem of 3D incompressible inviscid rotating Boussinesq equations ⋮ The 2D regularized incompressible Boussinesq equations with general critical dissipations ⋮ On some large solutions to the damped Boussinesq system ⋮ Global smooth solution to the 2D Boussinesq equations with fractional dissipation ⋮ The 2D inviscid Boussinesq equations with fractional diffusion in bounded domain

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global well-posedness of the 2D Boussinesq equations with vertical dissipation
• On the global well-posedness of a class of Boussinesq-Navier-Stokes systems
• Global well-posedness for the 2D inviscid Bénard system with fractional diffusivity and Yudovich's type data
• The 2D Boussinesq equations with logarithmically supercritical velocities
• Remarks on global regularity of the 2D Boussinesq equations with fractional dissipation
• Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation
• Initial-boundary value problem for two-dimensional viscous Boussinesq equations
• Blow-up criterion of smooth solutions for the Boussinesq equations
• Global well-posedness for a class of 2D Boussinesq systems with fractional dissipation
• Global regularity results for the 2D Boussinesq equations with partial dissipation
• Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
• Global well-posedness issues for the inviscid Boussinesq system with Yudovich's type data
• Global regularity of solutions of 2D Boussinesq equations with fractional diffusion
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• Global well-posedness of the viscous Boussinesq equations
• A maximum principle applied to quasi-geostrophic equations
• Nonlinear maximum principles for dissipative linear nonlocal operators and applications
• On a maximum principle and its application to the logarithmically critical Boussinesq system
• A global regularity result for the 2D Boussinesq equations with critical dissipation
• Eventual regularity of the two-dimensional Boussinesq equations with supercritical dissipation
• Global smooth solutions to the \(n\)-dimensional damped models of incompressible fluid mechanics with small initial datum
• Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation
• Yudovich type solution for the 2D inviscid Boussinesq system with critical and supercritical dissipation
• Small global solutions to the damped two-dimensional Boussinesq equations
• Generalized 2D Euler-Boussinesq equations with a singular velocity
• Global regularity for the 2D Boussinesq equations with partial viscosity terms
• Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion
• Vorticity and Incompressible Flow
• Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics
• Well-posedness and inviscid limits of the Boussinesq equations with fractional Laplacian dissipation
• GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO
• Fourier Analysis and Nonlinear Partial Differential Equations
• Global Well-Posedness for Euler–Boussinesq System with Critical Dissipation
• Nonlinear Schrödinger evolution equations
• Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations
• On the differentiability of the solution to an equation with drift and fractional diffusion
• The Two-Dimensional Incompressible Boussinesq Equations with General Critical Dissipation
• On the global regularity of the 2D Boussinesq equations with fractional dissipation
• Local well-posedness and blowup criterion of the Boussinesq equations in critical Besov spaces

This page was built for publication: Global regularity results of the 2D Boussinesq equations with fractional Laplacian dissipation