Blow-up criterion of smooth solutions for the Boussinesq equations

DOI10.1016/j.na.2014.07.022zbMath1300.35109OpenAlexW1989831121MaRDI QIDQ743858

Zhuan Ye

Publication date: 1 October 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2014.07.022

zbMATH Keywords

Boussinesq equationsblow-up criterionfractional 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) Blow-up in context of PDEs (35B44) Fractional partial differential equations (35R11)

Related Items (19)

On the global regularity of the 2D Boussinesq equations with fractional dissipation ⋮ Global existence and uniqueness of solutions to the three-dimensional Boussinesq equations ⋮ A logarithmically improved regularity criterion of smooth solutions for the 3D Boussinesq equations ⋮ Global regularity results of the 2D Boussinesq equations with fractional Laplacian dissipation ⋮ Regularity criterion of the 2D Bénard equations with critical and supercritical dissipation ⋮ Global regularity for a 3D Boussinesq model without thermal diffusion ⋮ Global regularity results for the 2D Boussinesq equations with partial dissipation ⋮ Global well-posedness for the 2D Euler-Boussinesq-Bénard equations with critical dissipation ⋮ A blowup criteria of smooth solutions to the 3D Boussinesq equations ⋮ Some new regularity criteria for the 2D Euler-Boussinesq equations via the temperature ⋮ Remarks on global regularity of the 2D Boussinesq equations with fractional dissipation ⋮ Remarks on the improved regularity criterion for the 2D Euler-Boussinesq equations with supercritical dissipation ⋮ The regularity criterion for weak solutions to the \(n\)-dimensional Boussinesq system ⋮ 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 ⋮ Remarks on pressure blow-up criterion of the 3D zero-diffusion Boussinesq equations in margin Besov spaces ⋮ Regularity criterion for a critical fractional diffusion model of two-dimensional micropolar flows ⋮ Global smooth solution to the 2D Boussinesq equations with fractional dissipation

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