Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations
| dc.creator | Cheng, Bin | |
| dc.creator | Tadmor, Eitan | |
| dc.date | 2007-06-06 | |
| dc.date.accessioned | 2026-07-07T08:04:18Z | |
| dc.date.available | 2026-07-07T08:04:18Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0706.0758 | |
| dc.identifier | http://arxiv.org/abs/0706.0758 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129907 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 76U05; 76E07; 76N10 | |
| dc.title | Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations | |
| dc.type | text |