Artículos de revistas
Weak stability of Lagrangian solutions to the semigeostrophic equations
Registro en:
Nonlinearity. Iop Publishing Ltd, v. 22, n. 10, n. 2521, n. 2539, 2009.
0951-7715
WOS:000269717000011
10.1088/0951-7715/22/10/011
Autor
Faria, JCO
Lopes, MC
Lopes, HJN
Institución
Resumen
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) 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. 22 10 2521 2539 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) CNPq [141.217/2004-9, 303.301/2007-4, 302.214/2004-6] FAPESP [2007/51490-7]