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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Weak stability of Lagrangian solutions to the semigeostrophic equations

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Author(s):
Faria, Josiane C. O. [1] ; Lopes Filho, Milton C. [1] ; Nussenzveig Lopes, Helena J. [1]
Total Authors: 3
Affiliation:
[1] Univ Estadual Campinas, IMECC, Dept Matemat, BR-13083970 Campinas, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Nonlinearity; v. 22, n. 10, p. 2521-2539, OCT 2009.
Web of Science Citations: 6
Abstract

In (Cullen and Feldman 2006 SIAM J. Math. Anal. 37 137-95), Cullen and Feldman proved the existence of Lagrangian solutions for the semigeostrophic system in physical variables with initial potential vorticity in L(p), p > 1. Here, we show that a subsequence of the Lagrangian solutions corresponding to a strongly convergent sequence of initial potential vorticities in L(1) converges strongly in L(q), q < infinity, to a Lagrangian solution, in particular extending the existence result of Cullen and Feldman to the case p = 1. We also present a counterexample for Lagrangian solutions corresponding to a sequence of initial potential vorticities converging in BM. The analytical tools used include techniques from optimal transportation, Ambrosio's results on transport by BV vector fields and Orlicz spaces. (AU)

FAPESP's process: 07/51490-7 - Mathematical aspects of incompressible fluid dynamics
Grantee:Milton da Costa Lopes Filho
Support Opportunities: Research Projects - Thematic Grants