The 2D Boussinesq equations with fractional horizontal dissipation and thermal diffusion

DOI10.1016/j.matpur.2018.01.006zbMath1392.35240OpenAlexW2783765331MaRDI QIDQ1639206

Zhuan Ye, Xiaojing Xu, Jiahong Wu

Publication date: 12 June 2018

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2018.01.006

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) A priori estimates in context of PDEs (35B45) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Fractional partial differential equations (35R11)

Related Items

Stability of 3D perturbations near a special 2D solution to the rotating Boussinesq equations ⋮ Stability of the 3D Boussinesq equations with partial dissipation near the hydrostatic balance ⋮ Temperature patches for a generalised 2D Boussinesq system with singular velocity ⋮ Stability and large-time behavior of the 2D Boussinesq equations with partial dissipation ⋮ On the global well‐posedness for the two‐dimensional Boussinesq equations with horizontal dissipation ⋮ Uniqueness result for the 3-D Navier-Stokes-Boussinesq equations with horizontal dissipation ⋮ A global regularity result for the 2D Boussinesq equations with critical dissipation ⋮ On some large solutions to the damped Boussinesq system ⋮ Optimal decay estimates for 2D Boussinesq equations with partial dissipation ⋮ Global well-posedness of the \(n\)-dimensional hyper-dissipative Boussinesq system without thermal diffusivity ⋮ Stability and exponential decay for the 2D anisotropic Boussinesq equations with horizontal dissipation ⋮ On the profiles of locally self-similar solutions for the 2D inviscid Boussinesq equations ⋮ Analysis of a singular Boussinesq model ⋮ On the global regularity for the anisotropic dissipative surface quasi-geostrophic equation ⋮ The 2D inviscid Boussinesq equations with fractional diffusion in bounded domain ⋮ The local existence of strong solution for the stochastic 3D Boussinesq equations ⋮ On the Boussinesq system: local well-posedness of the strong solution and inviscid limits ⋮ The stabilizing effect of the temperature on buoyancy-driven fluids ⋮ Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global well-posedness of the 2D Boussinesq equations with vertical dissipation
• Regularity results for the 2D Boussinesq equations with critical or supercritical dissipation
• On the global well-posedness of a class of Boussinesq-Navier-Stokes systems
• Global regularity results for the 2D Boussinesq equations with vertical dissipation
• Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation
• Global well-posedness for a class of 2D Boussinesq systems with fractional dissipation
• Global regularity results for the 2D Boussinesq equations with partial dissipation
• The 2D Boussinesq equations with vertical viscosity and vertical diffusivity
• On the global well-posedness of the Euler-Boussinesq system with fractional dissipation
• Global regularity of solutions of 2D Boussinesq equations with fractional diffusion
• Global regularity for the 2D micropolar equations with fractional dissipation
• Finite time blow up in the hyperbolic Boussinesq system
• Blowup with vorticity control for a 2D model of the Boussinesq equations
• Global well-posedness for the 2D fractional Boussinesq equations in the subcritical case
• Quasi-geostrophic equations, nonlinear Bernstein inequalities and \(\alpha\)-stable processes
• Global well-posedness of the viscous Boussinesq equations
• Nonlinear maximum principles for dissipative linear nonlocal operators and applications
• An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations
• Finite time blow up for a 1D model of 2D Boussinesq system
• Blowup in stagnation-point form solutions of the inviscid 2d Boussinesq equations
• Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation
• 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
• 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
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Global smooth solution to the 2D Boussinesq equations with fractional dissipation
• The Two-Dimensional Incompressible Boussinesq Equations with General Critical Dissipation
• Potentially singular solutions of the 3D axisymmetric Euler equations
• Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation