Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations

Details Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations

2007-06-06

arxiv.org/abs/0706.0758v1

Mathematics

Analysis of PDEs

Scientific paper

We study the stabilizing effect of rotational forcing in the nonlinear setting of two-dimensional shallow-water and more general models of compressible Euler equations. In [H. Liu and E. Tadmor, Phys. D 188 (2004), no. 3-4, 262-276] we have shown that the pressureless version of these equations admit global smooth solution for a large set of sub-critical initial configurations. In the present work we prove that when rotational force dominates the pressure, it \emph{prolongs} the life-span of smooth solutions for t < ln(1/d); here d << 1 is the ratio of the pressure gradient measured by the inverse squared Froude number, relative to the dominant rotational forces measured by the inverse Rossby number. Our study reveals a ``nearby'' periodic-in-time approximate solution in the small d-regime, upon which hinges the long time existence of the exact smooth solution. These results are in agreement with the close-to periodic dynamics observed in the ``near inertial oscillation'' (NIO) regime which follows oceanic storms. Indeed, our results indicate the existence of smooth, ``approximate periodic'' solution for a time period of \emph{days}, which is the relevant time period found in NIO obesrvations.

Affiliated with

Also associated with

No associations

Rating

Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-356608