Weak stability of Lagrangian solutions to the semigeostrophic equations

Autor(es)

Faria, Josiane C. O. ^[1] ; Lopes Filho, Milton C. ^[1] ; Nussenzveig Lopes, Helena J. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, IMECC, Dept Matemat, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Nonlinearity; v. 22, n. 10, p. 2521-2539, OCT 2009.
• Citações Web of Science: 6

Resumo

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)

• Processo FAPESP: 07/51490-7 - Aspectos matemáticos da dinâmica dos fluidos incompressíveis
• Beneficiário: Milton da Costa Lopes Filho
• Modalidade de apoio: Auxílio à Pesquisa - Temático