Blow-up criteria of smooth solutions to the 3D Boussinesq system with zero viscosity in a bounded domain

DOI10.1016/j.na.2012.01.008zbMath1243.35137OpenAlexW1968796118MaRDI QIDQ765854

Gen Nakamura, Jishan Fan, Haibing Wang

Publication date: 22 March 2012

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.2012.01.008

zbMATH Keywords

BMOblow-upregularity criterionBoussinesq system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (7)

Regularity criteria for the Boussinesq system with temperature-dependent viscosity and thermal diffusivity in a bounded domain ⋮ Regularity criteria via horizontal component of velocity for the Boussinesq equations in anisotropic Lorentz spaces ⋮ Regularity and attractors for the three‐dimensional generalized Boussinesq system ⋮ Regularity criteria and uniform estimates for the Boussinesq system with temperature-dependent viscosity and thermal diffusivity ⋮ Remarks on pressure blow-up criterion of the 3D zero-diffusion Boussinesq equations in margin Besov spaces ⋮ On the global regularity of \(N\)-dimensional generalized Boussinesq system. ⋮ Global existence of solutions for the three-dimensional Boussinesq system with anisotropic data

Cites Work

• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• On the blow-up of solutions of the 3-D Euler equations in a bounded domain
• A continuation principle for the 3-D Euler equations for incompressible fluids in a bounded domain
• A note on blow-up criterion to the 3-D Euler equations in a bounded domain
• The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
• Remarks on the Euler equation
• On blow-up criteria of smooth solutions to the 3-D Euler equations in a bounded domain.
• Uniqueness theorem for the basic nonstationary problem in the dynamics on an ideal incompressible fluid
• Local existence and blow-up criterion for the Boussinesq equations
• Geometric Properties and Nonblowup of 3D Incompressible Euler Flow
• REMARKS ON THE BLOW-UP CRITERION FOR THE 3-D BOUSSINESQ EQUATIONS
• Geometric constraints on potentially
• Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation
• Incompressible flows of an ideal fluid with unbounded vorticity
• Unnamed Item
• Unnamed Item

This page was built for publication: Blow-up criteria of smooth solutions to the 3D Boussinesq system with zero viscosity in a bounded domain