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 Lpt (L q x) 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...

The stability and accuracy of three methods which enforce either a divergence-free velocity field, density invariance, or their combination are tested here through the standard Taylor?Green and spin-down vortex problems. While various approaches to incompressible SPH (ISPH) have been proposed in the past decade, the present paper is restricted to the projection method for the pressure and veloc...

Dynamics of disparity vergence eye movements can be modified by adaptive stimuli that generate large transient disparities. These modifications were observed for convergence as well as divergence eye movements. After modification, the peak velocities of the step responses for convergence and divergence were substantially higher than in normal baseline responses, a change observed in all four su...

We consider transport properties for a class of periodic, Gaussian, stationary, divergence free, random velocity elds in R 2 with a nite number of spatial modes. Full asymptotics of the eeective diiusivity is obtained in the case of short time correlations, on a fully rigorous basis. Existence and uniqueness for a hypoellip-tic partial diierential equation coupling velocity Fourier modes to phy...

We obtain a regularity criteria of the solution to the three-dimensional magnetohydrodynamics system to remain smooth for all time involving only one velocity and one vorticity component. Moreover, the norm in space and time with which we impose our criteria for the vorticity component is at the scaling invariant level. The proof requires a new decomposition of the four nonlinear terms making u...

The Terrain Observation by Progressive Scans (TOPS) acquisition mode of the Sentinel-1 mission provides a wide coverage per acquisition with resolutions of 5 m in range and 20 m in azimuth, which makes this acquisition mode attractive for glacier velocity monitoring. Here, we retrieve surface velocities from the southern Ellesmere Island ice caps (Canadian Arctic) using both offset tracking and...

We consider the compressible Navier-Stokes system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. We derive the relative entropy inequality in the spirit of [7] for the system on moving domain and use it to prove the weak-strong uniqueness property.

By matching of repeat optical satellite images it is now possible to investigate glacier dynamics within large regions of the world and also between regions to improve knowledge about glacier dynamics in space and time. In this study we investigate whether the negative glacier mass balance seen over large parts of the world has caused the glaciers to change their speeds. The studied regions are...

We consider transport properties for Gaussian, stationary, divergence free, random velocity elds in R 2 , which are Markov in time. We prove the existence of eeective diiusivity. We also obtain its full asymptotics in the case of short time correlations, on a fully rigorous level. The main regularity assumption is that almost every realization of the random velocity eld should be continuous in ...

This paper describes a novel method to measure the differential invariants of the image velocity field from the integral of normal image velocities around image contours. This is equivalent to measuring the temporal changes in the area of a closed contour. This avoids having to recover a dense image velocity field and taking partial derivatives. It also does not require point or line correspond...