A Beale-Kato-Majda blow-up criterion for the 3-D compressible Navier-Stokes equations

DOI10.1016/j.matpur.2010.08.001zbMath1205.35212arXiv1001.1247OpenAlexW2964118263MaRDI QIDQ619890

Zhifei Zhang, Yongzhong Sun, Chao Wang

Publication date: 18 January 2011

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

Full work available at URL: https://arxiv.org/abs/1001.1247

zbMATH Keywords

compressible Navier-Stokes equations strong solution blow-up criterion Lamé system

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) A priori estimates in context of PDEs (35B45) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Blow-up in context of PDEs (35B44)

Related Items

Blowup criteria for full compressible Navier-Stokes equations with vacuum state ⋮ On classical solutions to 2D shallow water equations with degenerate viscosities ⋮ A blow-up criterion for 2D compressible nematic liquid crystal flows in terms of density ⋮ Refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure ⋮ Two characterizations of central BMO space via the commutators of Hardy operators ⋮ A regularity criterion of strong solutions to the 2D compressible magnetohydrodynamic equations ⋮ Blow-up criterion for two-dimensional viscous, compressible, and heat conducting magnetohydrodynamic flows ⋮ Ill-posedness for the compressible Navier-Stokes equations under barotropic condition in limiting Besov spaces ⋮ Global regularity for the 3D compressible magnetohydrodynamics with general pressure ⋮ Blow-up criterion for three-dimensional compressible viscoelastic fluids with vacuum ⋮ Global classical solutions of compressible isentropic Navier-Stokes equations with small density ⋮ Blowup analysis for two-dimensional viscous compressible, heat-conductive Navier-Stokes equations ⋮ Commutators of Hausdorff operators on Herz-type Hardy spaces ⋮ A blow-up criterion of strong solutions to the quantum hydrodynamic model ⋮ \(L^\infty\) continuation principle to the compressible non-isothermal nematic liquid crystal flows with zero heat conduction and vacuum ⋮ A strong solution of Navier-Stokes equations with a rotation effect for isentropic compressible fluids ⋮ On continuation criteria for the full compressible Navier-Stokes equations in Lorentz spaces ⋮ Convergence of a numerical method for the compressible Navier-Stokes system on general domains ⋮ Blow up criterion of strong solution for 3D viscous liquid-gas two-phase flow model with vacuum ⋮ Existence for the compressible magnetohydrodynamic equations with vacuum ⋮ A Beale-Kato-Majda criterion for three dimensional compressible viscous non-isentropic magnetohydrodynamic flows without heat-conductivity ⋮ Mass concentration phenomenon to the two-dimensional Cauchy problem of the compressible magnetohydrodynamic equations ⋮ Compressible fluid motion with uncertain data ⋮ A regularity criterion for the 3D full compressible magnetohydrodynamic equations with zero heat conductivity ⋮ Serrin-type blowup criterion for viscous, compressible, and heat conducting Navier-Stokes and magnetohydrodynamic flows ⋮ Existence results and blow-up criterion of compressible radiation hydrodynamic equations ⋮ A regularity criterion for the \(3D\) full compressible Navier-Stokes-Maxwell system in a bounded domain ⋮ Blow-up criterion for the 3D non-resistive compressible magnetohydrodynamic equations ⋮ Relative entropies, suitable weak solutions, and weak-strong uniqueness for the compressible Navier-Stokes system ⋮ Blow-up criteria for three-dimensional compressible radiation hydrodynamics equations with vacuum ⋮ Global classical solution to the three-dimensional isentropic compressible Navier-Stokes equations with general initial data ⋮ A new blowup criterion for strong solutions of the three-dimensional isentropic compressible micropolar fluid ⋮ Singularity formation to the two-dimensional compressible non-isothermal nematic liquid crystal flows in a bounded domain ⋮ A characterization of central BMO space via the commutator of fractional Hardy operator ⋮ Weighted estimates for commutators of Hausdorff operators on the Heisenberg group ⋮ Blowup criteria for strong solutions to the compressible Navier-Stokes equations with variable viscosity ⋮ Global well-posedness of classical solutions to the compressible Navier-Stokes equations in a half-space ⋮ Serrin-type blowup criterion for full compressible Navier-Stokes system ⋮ Serrin-type blowup criterion for full compressible Navier-Stokes-Maxwell system with vacuum ⋮ A blow-up criterion for a 2D viscous liquid-gas two-phase flow model ⋮ Uniform global solutions of the 3D compressible MHD system in a bounded domain ⋮ A blow-up criterion of strong solutions to a viscous liquid-gas two-phase flow model with vacuum in 3D ⋮ Blow-up criterions of strong solutions to 3D compressible Navier-Stokes equations with vacuum ⋮ Blow-up criterion for 3D viscous liquid-gas two-phase flow model ⋮ Decay estimates for isentropic compressible Navier-Stokes equations in bounded domain ⋮ A continuation principle to the Cauchy problem of two-dimensional compressible Navier-Stokes equations with variable viscosity ⋮ A new blowup criterion for strong solutions of the compressible nematic liquid crystal flow ⋮ Regularity and uniqueness for the compressible full Navier-Stokes equations ⋮ A blow-up criterion of strong solutions to the compressible viscous heat-conductive flows with zero heat conductivity ⋮ Weak Serrin-type blowup criterion for three-dimensional nonhomogeneous viscous incompressible heat conducting flows ⋮ Strong solutions of the compressible nematic liquid crystal flow ⋮ Global well-posedness of compressible Navier-Stokes equations for some classes of large initial data ⋮ Corrigendum: ``A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of density ⋮ A blow-up criterion for 3D non-resistive compressible magnetohydrodynamic equations with initial vacuum ⋮ A remark on blow-up criterion for 3D compressible magnetohydrodynamic flows with vacuum ⋮ Blow-up criterion for the 3D compressible non-isentropic Navier-Stokes equations without thermal conductivity ⋮ On the global existence of classical solutions for compressible Navier-Stokes equations with vacuum ⋮ Blowup mechanism for viscous compressible heat-conductive magnetohydrodynamic flows in three dimensions ⋮ Blow-up criterion for the 3D viscous polytropic fluids with degenerate viscosities ⋮ A new blowup criterion for strong solutions to a viscous liquid-gas two-phase flow model with vacuum in three dimensions ⋮ A blowup criterion for the 2D \(k\)-\(\epsilon\) model equations for turbulent flows ⋮ Dissipative measure-valued solutions to the compressible Navier-Stokes system ⋮ On center singularity for compressible spherically symmetric nematic liquid crystal flows ⋮ Global existence for a class of large solution to the three-dimensional micropolar fluid equations with vacuum ⋮ A characterization of Campanato space via commutator of fractional integral ⋮ Mass concentration phenomenon to the 2D Cauchy problem of the compressible Navier-Stokes equations ⋮ Global well-posedness of 2D compressible Navier-Stokes equations with large data and vacuum ⋮ A blow-up criterion of strong solutions to the 3D compressible MHD equations with vacuum ⋮ On scaling invariance and type-I singularities for the compressible Navier-Stokes equations ⋮ A multi-fluid compressible system as the limit of weak solutions of the isentropic compressible Navier-Stokes equations ⋮ A Beale-Kato-Majda criterion for three-dimensional compressible viscous heat-conductive flows ⋮ A regularity criterion for the 2D full compressible MHD equations with zero heat conductivity ⋮ Blow up criterion for compressible nematic liquid crystal flows in dimension three ⋮ Blow-up criterion and the global existence of strong/classical solutions to Navier-Stokes/Allen-Cahn system ⋮ On formation of singularity for full compressible Navier-Stokes system with zero heat conduction ⋮ Singularity formation to the two-dimensional non-barotropic non-resistive magnetohydrodynamic equations with zero heat conduction in a bounded domain ⋮ One new blowup criterion for the 2D full compressible Navier-Stokes system ⋮ Global regularity for the Cauchy problem of three-dimensional compressible magnetohydrodynamics equations ⋮ Existence and uniqueness of weak solutions of the compressible spherically symmetric Navier-Stokes equations ⋮ Singularity formation to the two-dimensional non-resistive compressible magnetohydrodynamic equations in a bounded domain ⋮ Refined blow-up criteria for the full compressible Navier-Stokes equations involving temperature ⋮ Global existence of strong solution to the chemotaxis-shallow water system with vacuum in a bounded domain ⋮ Existence and a blow-up criterion of solution to the 3D compressible Navier-Stokes-Poisson equations with finite energy ⋮ Review on mathematical analysis of some two-phase flow models ⋮ A blow-up criterion of strong solution to a 3D viscous liquid-gas two-phase flow model with vacuum ⋮ A blow-up criterion for two dimensional compressible viscous heat-conductive flows ⋮ Global existence of classical solutions to the two-dimensional compressible Boussinesq equations in a square domain ⋮ Global strong solution to the two-dimensional full compressible Navier-Stokes equations with large viscosity ⋮ Global existence of classical solutions for two-dimensional isentropic compressible Navier-Stokes equations with small initial mass ⋮ Global strong solutions to the two-dimensional full compressible Navier-Stokes equations with vacuum ⋮ Global stability of large solutions to the 3D compressible Navier-Stokes equations ⋮ Convergence and error estimates for a finite difference scheme for the multi-dimensional compressible Navier-Stokes system ⋮ A blowup criterion for the compressible nematic liquid crystal flows in dimension two ⋮ Optimal decay of compressible Navier-Stokes equations with or without potential force ⋮ A characterization on breakdown of smooth spherically symmetric solutions of the isentropic system of compressible Navier-Stokes equations ⋮ Global regularity to the two dimensional compressible Navier-Stokes equations with mass diffusion ⋮ Large-time behavior for compressible Navier-Stokes-Fourier system in the whole space ⋮ The optimal decay rate of strong solution for the compressible Navier-Stokes equations with large initial data ⋮ The Navier-Stokes-Vlasov-Fokker-Planck system in bounded domains ⋮ On formation of singularity for non-isentropic Navier-Stokes equations without heat-conductivity ⋮ A BLOW-UP CRITERION FOR 3D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM ⋮ Global solutions to an initial boundary problem for the compressible 3D MHD equations with Navier-slip and perfectly conducting boundary conditions in exterior domains ⋮ Wellposedness and zero microrotation viscosity limit of the 2D micropolar fluid equations ⋮ Blow‐up criterion for 3D viscous‐resistive compressible magnetohydrodynamic equations ⋮ L^∞continuation principle to the non-baratropic non-resistive magnetohydrodynamic equations without heat conductivity ⋮ A blowup criterion for viscous, compressible, and heat-conductive magnetohydrodynamic flows ⋮ On the Cauchy problem of the full Navier-Stokes equations for three-dimensional compressible viscous heat-conducting flows subject to large external potential forces ⋮ Global existence and large time behavior for the 2-D compressible Navier-Stokes equations without heat conductivity ⋮ Singularity formation to the 2D Cauchy problem of nonbarotropic magnetohydrodynamic equations without heat conductivity ⋮ Local well‐posedness for an isentropic compressible Ginzburg–Landau–Navier–Stokes with vacuum ⋮ Global solutions of \(2D\) isentropic compressible Navier-Stokes equations with one slow variable ⋮ Formation of singularity for full compressible magnetohydrodynamic equations with zero resistivity in two dimensional bounded domains ⋮ Blow up criteria for the 2D compressible Navier-Stokes equations in bounded domains with vacuum ⋮ Unnamed Item ⋮ Global solutions of 3D isentropic compressible Navier-Stokes equations with two slow variables ⋮ Convergence of a stochastic collocation finite volume method for the compressible Navier-Stokes system ⋮ Some Serrin type blow‐up criteria for the three‐dimensional viscous compressible flows with large external potential force ⋮ Existence and blow up criterion for strong solutions to the compressible biaxial nematic liquid crystal flow ⋮ Calderón–Zygmund theory in Lorentz mixed‐norm spaces and its application to compressible fluids ⋮ A regularity condition of strong solutions to the two-dimensional equations of compressible nematic liquid crystal flows ⋮ Conditional regularity for the Navier-Stokes-Fourier system with Dirichlet boundary conditions ⋮ A general sufficient criterion for energy conservation in the Navier–Stokes system ⋮ On the regularity criteria for the three‐dimensional compressible Navier–Stokes system in Lorentz spaces ⋮ Blow-up criteria for a fluid dynamical model arising in astrophysics ⋮ Global existence for a class of large solution to compressible Navier-Stokes equations with vacuum ⋮ Improved error estimates for the finite volume and the MAC schemes for the compressible Navier-Stokes system ⋮ Relative Entropy, Weak-Strong Uniqueness, and Conditional Regularity for a Compressible Oldroyd--B Model ⋮ Mass concentration phenomenon in the 3D bipolar compressible Navier-Stokes-Poisson system ⋮ Global well-posedness and exponential decay rates of the strong solutions to the two-dimensional full compressible magnetohydrodynamics equations with vacuum in some class of large initial data ⋮ Blowup of smooth solution for non-isentropic magnetohydrodynamic equations without heat conductivity ⋮ Weak Serrin‐type criterion for the three‐dimensional viscous compressible Navier–Stokes system ⋮ Blow-up of smooth solutions to the isentropic compressible MHD equations ⋮ Global classical solutions of viscous liquid–gas two‐phase flow model ⋮ Global existence of classical solutions to two‐dimensional Navier–Stokes equations with Cauchy data containing vacuum ⋮ Blow up criteria for the compressible Navier–Stokes equations ⋮ On formation of singularity of the full compressible magnetohydrodynamic equations with zero heat conduction ⋮ Convergence of a finite volume scheme for the compressible Navier–Stokes system ⋮ Well-posedness for compressible MHD systems with highly oscillating initial data ⋮ Blow up criterion for the 2D full compressible Navier–Stokes equations involving temperature in critical spaces ⋮ ILL-POSEDNESS FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH THE VELOCITY IN FRAMEWORK ⋮ A Serrin criterion for compressible nematic liquid crystal flows ⋮ Strong solutions of 3D compressible Oldroyd-B fluids ⋮ Compactness of the Commutators of Fractional Hardy Operator with Rough Kernel ⋮ On Classical Solutions of the Compressible Magnetohydrodynamic Equations with Vacuum ⋮ Blow-up Criteria for the 2D Full Compressible MHD system

Cites Work