Displaying similar documents to “On the instantaneous spreading for the Navier–Stokes system in the whole space”

Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity

Alexis Vasseur (2009)

Applications of Mathematics

Similarity:

In this short note we give a link between the regularity of the solution u to the 3D Navier-Stokes equation and the behavior of the direction of the velocity u / | u | . It is shown that the control of Div ( u / | u | ) in a suitable L t p ( L x q ) norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin and Fefferman. However, in this case the condition is not on the vorticity but on the velocity itself. The proof, based...

Non-autonomous 2D Navier–Stokes system with a simple global attractor and some averaging problems

V. V. Chepyzhov, M. I. Vishik (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study the global attractor of the non-autonomous 2D Navier–Stokes system with time-dependent external force g ( x , t ) . We assume that g ( x , t ) is a translation compact function and the corresponding Grashof number is small. Then the global attractor has a simple structure: it is the closure of all the values of the unique bounded complete trajectory of the Navier–Stokes system. In particular, if g ( x , t ) is a quasiperiodic function with respect to t , then the attractor is a continuous image of a torus....