LONG-TIME EXISTENCE OF SMOOTH SOLUTIONS FOR THLong time existence of smooth solutions for the rapidly rotating shallow-water and Euler equationsE
| dc.contributor.author | CHENG, BIN | |
| dc.contributor.author | TADMOR, EITAN | |
| dc.date.accessioned | 2008-11-03T18:49:28Z | |
| dc.date.available | 2008-11-03T18:49:28Z | |
| dc.date.issued | 2008 | |
| dc.description.abstract | 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 [Phys. D, 188 (2004), pp. 262–276] Liu and Tadmor have shown that the pressureless version of these equations admit a global smooth solution for a large set of subcritical initial configurations. In the present work we prove that when rotational force dominates the pressure, it prolongs the lifespan of smooth solutions for t ≲ ln(δ^−1); here δ ≪ 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 δ 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 a smooth, “approximate periodic” solution for a time period of days, which is the relevant time period found in NIO observations. | en |
| dc.format.extent | 222881 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | B. Cheng & E. Tadmor (2007). Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations. SIAM Journal on Mathematical Analysis 39(5) (2008) 1668-1685. | en |
| dc.identifier.uri | http://hdl.handle.net/1903/8663 | |
| dc.language.iso | en_US | en |
| dc.publisher | Copyright: Society for Industrial and Applied Mathematics | en |
| dc.relation.isAvailableAt | College of Computer, Mathematical & Physical Sciences | en_us |
| dc.relation.isAvailableAt | Mathematics | en_us |
| dc.relation.isAvailableAt | Digital Repository at the University of Maryland | en_us |
| dc.relation.isAvailableAt | University of Maryland (College Park, MD) | en_us |
| dc.subject | shallow-water equations | en |
| dc.subject | rapid rotation | en |
| dc.subject | pressureless equations | en |
| dc.subject | critical threshold | en |
| dc.subject | two-dimensinoal Euler equations | en |
| dc.subject | long-time existence | en |
| dc.title | LONG-TIME EXISTENCE OF SMOOTH SOLUTIONS FOR THLong time existence of smooth solutions for the rapidly rotating shallow-water and Euler equationsE | en |
| dc.type | Article | en |