REMARKS ON THE BLOW-UP CRITERION FOR THE 3-D BOUSSINESQ EQUATIONS

DOI10.1142/S0218202599000580zbMath1034.35113MaRDI QIDQ4799026

Naoyuki Ishimura, Hiroko Morimoto

Publication date: 16 March 2003

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

Boussinesq equationsblow-up of smooth solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05)

Related Items

Global well-posedness for 3D generalized Navier-Stokes-Boussinesq equations ⋮ Global existence and uniqueness of solutions to the three-dimensional Boussinesq equations ⋮ Serrin-type blow-up criteria for 3D Boussinesq equations ⋮ Well-posedness for density-dependent Boussinesq equations without dissipation terms in Besov spaces ⋮ A regularity criterion for the 3D Boussinesq equations ⋮ Blow-up criteria for three-dimensional Boussinesq equations in Triebel-Lizorkin spaces ⋮ A logarithmically improved regularity criterion for the 3D Boussinesq equations via the pressure ⋮ Regularity criteria via horizontal component of velocity for the Boussinesq equations in anisotropic Lorentz spaces ⋮ Blow-up criterion of solutions of the horizontal viscous primitive equations with horizontal eddy diffusivity ⋮ A blowup criteria of smooth solutions to the 3D Boussinesq equations ⋮ Time decay and stability of solutions for the 3D density-dependent incompressible Boussinesq system ⋮ Higher order regularity and blow-up criterion for semi-dissipative and ideal Boussinesq equations ⋮ A remark on the regularity criterion for the 3D Boussinesq equations involving the pressure gradient ⋮ Some regularity criteria for the 3D Boussinesq equations in the class \(L^2(0,T;\dot B^{-1}_{\infty,\infty})\) ⋮ Local existence and blow‐up criterion for the generalized Boussinesq equations in Besov spaces ⋮ Blow-up criteria and regularity criterion for the three-dimensional magnetic Bénard system in the multiplier space ⋮ Logarithmical regularity criterion of the three-dimensional Boussinesq equations in terms of the pressure ⋮ Regularity criteria of the 3D Boussinesq equations in the Morrey-Campanato space ⋮ A note on the regularity criterion of the two-dimensional Newton-Boussinesq equations ⋮ A blow-up criterion for 3D Boussinesq equations in Besov spaces ⋮ Blow-up criteria for 3D Boussinesq equations in the multiplier space ⋮ A regularity criterion to the 3D Boussinesq equations ⋮ On the regularity criterion for the 2D Boussinesq equations involving the temperature ⋮ Remarks on pressure blow-up criterion of the 3D zero-diffusion Boussinesq equations in margin Besov spaces ⋮ Regularity criterion for 3D Boussinesq equations via partial horizontal derivatives of two velocity components ⋮ Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces with negative indices ⋮ A regularity criterion of weak solutions to the 3D Boussinesq equations ⋮ On the regularity of weak solutions of the Boussinesq equations in Besov spaces ⋮ A regularity criterion of weak solutions to the 3D Boussinesq equations ⋮ Blow-up criterion of smooth solutions for the Boussinesq equations ⋮ A note on regularity criterion for the 3D Boussinesq system with partial viscosity ⋮ Unnamed Item ⋮ On the blow-up criterion for the 3D Boussinesq system with zero viscosity constant ⋮ Blow-up criteria of smooth solutions to the 3D Boussinesq system with zero viscosity in a bounded domain ⋮ Zero dissipation limit and stability of boundary layers for the heat conductive Boussinesq equations in a bounded domain ⋮ Blow-up criteria of smooth solutions to the 3D Boussinesq equations ⋮ Logarithmically improved regularity criteria for the Boussinesq equations ⋮ A remark on the regularity criterion of Boussinesq equations with zero heat conductivity ⋮ On the Boussinesq system: local well-posedness of the strong solution and inviscid limits

Cites Work

• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• Remarks on a paper by J. T. Beale, T. Kato, and A. Majda (Remarks on the breakdown of smooth solutions for the 3-dimensional Euler equations)
• Note on loss of regularity for solutions of the 3-D incompressible Euler and related equations
• On the existence and uniqueness of the stationary solution to the equations of natural convection
• Global solutions for the heat convection equations in an exterior domain
• On weak solutions of nonstationary Boussinesq equations
• The Eckhaus criterion for convection roll solutions of the Oberbeck-Boussinesq equations
• Nonstationary flows of viscous and ideal fluids in \(R^3\)
• Length scales in solutions of the Navier-Stokes equations
• Vorticity and the mathematical theory of incompressible fluid flow
• Attractors for the Bénard problem: existence and physical bounds on their fractal dimension
• Commutator estimates and the euler and navier-stokes equations
• Ladder theorems for the 2D and 3D Navier-Stokes equations on a finite periodic domain
• Vorticity, Turbulence, and Acoustics in Fluid Flow
• Local existence and blow-up criterion for the Boussinesq equations
• Small-scale structures in Boussinesq convection
• Two-dimensional Rayleigh-Benard convection