Regularity criteria of the 2D fractional Boussinesq equations in the supercritical case

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Hydrology, hydrography, oceanography (86A05) Stability in context of PDEs (35B35) Fractional derivatives and integrals (26A33) Fractional partial differential equations (35R11)

Cites Work

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Regularity results for the 2D Boussinesq equations with critical or supercritical dissipation
Regularity criteria for the 2D Boussinesq equations with supercritical dissipation
On the global well-posedness of a class of Boussinesq-Navier-Stokes systems
Remarks on the improved regularity criterion for the 2D Euler-Boussinesq equations with supercritical dissipation
Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation
Blow-up criterion of smooth solutions for the Boussinesq equations
Global well-posedness for a class of 2D Boussinesq systems with fractional dissipation
On the global well-posedness of the Euler-Boussinesq system with fractional dissipation
Factorization theorems for Hardy spaces in several variables
On the differentiability issue of the drift-diffusion equation with nonlocal Lévy-type diffusion
Global well-posedness for the 2D fractional Boussinesq equations in the subcritical case
On Kato-Ponce and fractional Leibniz
Global well-posedness of the viscous Boussinesq equations
Nonlinear maximum principles for dissipative linear nonlocal operators and applications
A global regularity result for the 2D Boussinesq equations with critical dissipation
A regularity criterion for the three-dimensional MHD equations in terms of one directional derivative of the pressure
An alternative approach to global regularity for the 2D Euler-Boussinesq equations with critical dissipation
A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation
Yudovich type solution for the 2D inviscid Boussinesq system with critical and supercritical dissipation
Global regularity for the 2D Boussinesq equations with partial viscosity terms
On the regularity criterion for the 2D Boussinesq equations involving the temperature
Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics
Fourier Analysis and Nonlinear Partial Differential Equations
Global Well-Posedness for Euler–Boussinesq System with Critical Dissipation
Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations
Local existence and blow-up criterion for the Boussinesq equations
On the differentiability of the solution to an equation with drift and fractional diffusion
Local well-posedness and blow up criterion for the Inviscid Boussinesq system in H\"{o}lder spaces
Classical Fourier Analysis
The Two-Dimensional Incompressible Boussinesq Equations with General Critical Dissipation
Local well-posedness and blowup criterion of the Boussinesq equations in critical Besov spaces
Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation
A new version of the generalized F-expansion method for the fractional Biswas-Arshed equation and Boussinesq equation with the beta-derivative

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