Regularity criteria of Leray-Hopf weak solutions to the three-dimensional Navier-Stokes equations in some critical spaces such as Lorentz space, Morrey space and multiplier space are derived in terms of two partial de...Regularity criteria of Leray-Hopf weak solutions to the three-dimensional Navier-Stokes equations in some critical spaces such as Lorentz space, Morrey space and multiplier space are derived in terms of two partial derivatives, θ1u1, θ2u2, of velocity fields.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.
In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space B ∞,∞ -r （R2）. The result shows that if 0 is a weak solutions satisfies ...In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space B ∞,∞ -r （R2）. The result shows that if 0 is a weak solutions satisfies ∫ 0 T ｜｜ θ （·,s）｜｜a/a-r B ∞,∞ -r /（1＋ln（e＋｜｜ ⊥（·,s）｜｜ L r2） ds〈∞ for some 0〈r〈a and 0〈a〈1,then θ is regular at t = T. In view of the embedding L 2/r M p 2/r B ∞,∞ -r with 2≤p〈2/r and 0≤r〈1, we see that our result extends the results due to [20] and [31].展开更多
In this note, we will give a new proof of the blow-up criterion of smooth solutions to the 3D incompressible magneto-hydrodynamic equations by a simple application of Gagliardo-Nirenberg＇ s inequality.
In this paper, we study the blow-up criterion of smooth solutions to the 3D magneto-hydrodynamic system in B^0∞,∞. We show that a smooth solution of the 3D MHD equations with zero kinematic viscosity in the whole sp...In this paper, we study the blow-up criterion of smooth solutions to the 3D magneto-hydrodynamic system in B^0∞,∞. We show that a smooth solution of the 3D MHD equations with zero kinematic viscosity in the whole space R3 breaks down if and only if certain norm of the vorticity blows up at the same time.展开更多
基金supported by the NSF of China (10801001)NSF of Anhui Province (11040606M02) the 211 Project of Anhui University (KJTD002B, KJJQ005)
文摘Regularity criteria of Leray-Hopf weak solutions to the three-dimensional Navier-Stokes equations in some critical spaces such as Lorentz space, Morrey space and multiplier space are derived in terms of two partial derivatives, θ1u1, θ2u2, of velocity fields.
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.
文摘In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space B ∞,∞ -r （R2）. The result shows that if 0 is a weak solutions satisfies ∫ 0 T ｜｜ θ （·,s）｜｜a/a-r B ∞,∞ -r /（1＋ln（e＋｜｜ ⊥（·,s）｜｜ L r2） ds〈∞ for some 0〈r〈a and 0〈a〈1,then θ is regular at t = T. In view of the embedding L 2/r M p 2/r B ∞,∞ -r with 2≤p〈2/r and 0≤r〈1, we see that our result extends the results due to [20] and [31].
文摘In this note, we will give a new proof of the blow-up criterion of smooth solutions to the 3D incompressible magneto-hydrodynamic equations by a simple application of Gagliardo-Nirenberg＇ s inequality.
文摘In this paper, we study the blow-up criterion of smooth solutions to the 3D magneto-hydrodynamic system in B^0∞,∞. We show that a smooth solution of the 3D MHD equations with zero kinematic viscosity in the whole space R3 breaks down if and only if certain norm of the vorticity blows up at the same time.
