In this paper, we consider the short time classical solution to a simplified hydro-dynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establisha criterion for possible breakdown of such s...In this paper, we consider the short time classical solution to a simplified hydro-dynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establisha criterion for possible breakdown of such solutions at a finite time. More precisely, if （u, d）is smooth up to time T provided that ∫T 0‖△×u（t, ·）‖BMO（R3） ＋‖△d（t, ·）‖8L4（R3）dt 〈∞.展开更多
In this paper,we prove a blow-up criterion of strong solutions to the 3-D viscous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum.This blow-up criterion depen...In this paper,we prove a blow-up criterion of strong solutions to the 3-D viscous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum.This blow-up criterion depends only on the gradient of velocity and the temperature,which is similar to the one for compressible Navier-Stokes equations.展开更多
In this article, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations. A blow-up criterion in terms of the maximum norm of gradients of velocity is obtained for the spheric...In this article, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations. A blow-up criterion in terms of the maximum norm of gradients of velocity is obtained for the spherically symmetric strong solution in terms of the regularity estimates near the symmetric center and the free boundary respectively.展开更多
In this note, we prove that Xr （0 〈 r 〈 1） norm of the vorticity controls the blow-up phenomena of strong solutions to the Navier-Stokes equations in R3.
We investigate the local existence of smooth solutions of a 3D ideal magneto-hydrodynamics （MHD） equations in a bounded domain and give a blow-up criteria to thisequations with respect to vorticists.
In this paper, we study the fifth-order Camassa-Holm equation with weakly dissipative term. We first give the local well-posedness result and the blow up criterion. Then, we establish sufficient conditions to guarante...In this paper, we study the fifth-order Camassa-Holm equation with weakly dissipative term. We first give the local well-posedness result and the blow up criterion. Then, we establish sufficient conditions to guarantee that the solution exists globally in time. Finally, the infinite propagation speed of this equation is also investigated.展开更多
In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let （u（x,t）,b（x,t）） be smooth solutions in （0, T）. It is shown that the solution...In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let （u（x,t）,b（x,t）） be smooth solutions in （0, T）. It is shown that the solution （u（x, t）, b（x, t）） can be extended beyond t = T if （u（x,t）, b（x, t）） ∈ L^1 （0, T; BMO） or the vorticity （rot u（x, t）, rot b（x, t）） ∈ L^1 （0, T; BMO） or the deformation （Def u（x, t）, Def b（x, t）） ∈ L^1 （0, T; BMO）.展开更多
In this paper, we study a Cauchy problem for the equations of 3D compressible viscoelastic fluids with vacuum. We establish a blow-up criterion for the local strong solutions in terms of the upper bound of the density...In this paper, we study a Cauchy problem for the equations of 3D compressible viscoelastic fluids with vacuum. We establish a blow-up criterion for the local strong solutions in terms of the upper bound of the density and deformation gradient.展开更多
基金supported by the Natural Science Key Foundation of Universities of Fujian Province(JZ160406)Natural Science Foundation of Fujian Province(2015J01582)
文摘In this paper, we consider the short time classical solution to a simplified hydro-dynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establisha criterion for possible breakdown of such solutions at a finite time. More precisely, if （u, d）is smooth up to time T provided that ∫T 0‖△×u（t, ·）‖BMO（R3） ＋‖△d（t, ·）‖8L4（R3）dt 〈∞.
基金supported by NSFC (11171228,10801111,10971171)the fundamental Research Funds for the Central University (2010121006)the Natural Science Foundation of Fujian Province of China (2010J05011)
文摘In this paper,we prove a blow-up criterion of strong solutions to the 3-D viscous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum.This blow-up criterion depends only on the gradient of velocity and the temperature,which is similar to the one for compressible Navier-Stokes equations.
基金supported by the NNSFC(11171228,11231006,and 11225102)NSFC-RGC Grant 11461161007the Key Project of Beijing Municipal Education Commission No.CIT&TCD20140323
文摘In this article, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations. A blow-up criterion in terms of the maximum norm of gradients of velocity is obtained for the spherically symmetric strong solution in terms of the regularity estimates near the symmetric center and the free boundary respectively.
文摘In this note, we prove that Xr （0 〈 r 〈 1） norm of the vorticity controls the blow-up phenomena of strong solutions to the Navier-Stokes equations in R3.
基金supported by NRF-2015R1A5A1009350the National Research Foundation of Korea Grant funded by the Korean Government(NRF-2016R1D1A1B03930422)
文摘We investigate the local existence of smooth solutions of a 3D ideal magneto-hydrodynamics （MHD） equations in a bounded domain and give a blow-up criteria to thisequations with respect to vorticists.
文摘In this paper, we study the fifth-order Camassa-Holm equation with weakly dissipative term. We first give the local well-posedness result and the blow up criterion. Then, we establish sufficient conditions to guarantee that the solution exists globally in time. Finally, the infinite propagation speed of this equation is also investigated.
基金Supported by the National Natural Science Foundation of China （No.10571016） and Science Foundation for the Excellent Young Teacher of Henan Province.
文摘In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let （u（x,t）,b（x,t）） be smooth solutions in （0, T）. It is shown that the solution （u（x, t）, b（x, t）） can be extended beyond t = T if （u（x,t）, b（x, t）） ∈ L^1 （0, T; BMO） or the vorticity （rot u（x, t）, rot b（x, t）） ∈ L^1 （0, T; BMO） or the deformation （Def u（x, t）, Def b（x, t）） ∈ L^1 （0, T; BMO）.
文摘In this paper, we study a Cauchy problem for the equations of 3D compressible viscoelastic fluids with vacuum. We establish a blow-up criterion for the local strong solutions in terms of the upper bound of the density and deformation gradient.
