Global well-posedness for a class of 2D Boussinesq systems with fractional dissipation

DOI10.1016/j.jde.2014.08.006zbMath1300.35108OpenAlexW2051235788MaRDI QIDQ743895

Wanrong Yang, Jiahong Wu, Quan-sen Jiu

Publication date: 1 October 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2014.08.006

zbMATH Keywords

global regularity2D Boussinesq equationsfractional dissipation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Fractional derivatives and integrals (26A33) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Fractional partial differential equations (35R11)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the global well-posedness of a class of Boussinesq-Navier-Stokes systems
• The 2D Boussinesq equations with logarithmically supercritical velocities
• Global regularity results for the 2D Boussinesq equations with vertical dissipation
• Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation
• Initial-boundary value problem for two-dimensional viscous Boussinesq equations
• The 2D Boussinesq equations with vertical viscosity and vertical diffusivity
• 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
• Infinite Prandtl number convection
• 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
• 2D inviscid heat conductive Boussinesq equations on a bounded domain
• Eventual regularity of the two-dimensional Boussinesq equations with supercritical dissipation
• Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical 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
• Large time decay and growth for solutions of a viscous Boussinesq system
• 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
• Some Remarks on Topological Fluid Mechanics
• Small-scale structures in Boussinesq convection
• Local well-posedness and blow up criterion for the Inviscid Boussinesq system in H\"{o}lder spaces

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