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|Type:||Artigo de periódico|
|Title:||Weak Stability Of Lagrangian Solutions To The Semigeostrophic Equations|
Lopes Filho M.C.
Nussenzveig Lopes H.J.
|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 Lp, p > 1. Here, we show that a subsequence of the Lagrangian solutions corresponding to a strongly convergent sequence of initial potential vorticities in L1 converges strongly in Lq, q < ∞, 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 . The analytical tools used include techniques from optimal transportation, Ambrosio's results on transport by BV vector fields and Orlicz spaces. © 2009 IOP Publishing Ltd and London Mathematical Society.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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