42 research outputs found
Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor
In this paper we provide a sufficient condition, in terms of only one of the
nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity
vector field, for the global regularity of strong solutions to the
three-dimensional Navier-Stokes equations in the whole space, as well as for
the case of periodic boundary conditions
The optimal temporal decay estimates for the fractional power dissipative equation in negative Besov spaces
Global existence of discretely self-similar solutions to the generalized MHD system in Besov space
Lower bounds on blow up solutions of the three-dimensional Navier–Stokes equations in homogeneous Sobolev spaces
Suppose that u(t) is a solution of the three-dimensional Navier–Stokes equations, either on the whole space or with periodic boundary conditions, that has a singularity at time T. In this paper we show that the norm of u(T − t) in the homogeneous Sobolev space s must be bounded below by cst−(2s−1)/4 for 1/2 5/2. (The result for 1/2 < s < 3/2 follows from well-known lower bounds on blowup in Lp spaces.) We show in particular that the local existence time in s(3) depends only on the s-norm for 1/2 < s < 5/2, s ≠3/2