Weak stability of Lagrangian solutions to the semigeostrophic equations Export

@article{citeulike:5790627, 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 \mathcal{BM} . The analytical tools used include techniques from optimal transportation, Ambrosio's results on transport by BV vector fields and Orlicz spaces.}, author = {Faria, Josiane C. O. and Filho, Milton C. and Lopes, Helena J.}, citeulike-article-id = {5790627}, citeulike-linkout-0 = {http://dx.doi.org/10.1088/0951-7715/22/10/011}, doi = {10.1088/0951-7715/22/10/011}, journal = {Nonlinearity}, keywords = {semi-geostrophic}, number = {10}, pages = {2521--2539}, posted-at = {2009-09-16 07:51:41}, priority = {2}, title = {Weak stability of Lagrangian solutions to the semigeostrophic equations}, url = {http://dx.doi.org/10.1088/0951-7715/22/10/011}, volume = {22}, year = {2009} }

TY - JOUR ID - citeulike:5790627 L3 - citeulike-article-id:5790627 N2 - 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 \mathcal{BM} . The analytical tools used include techniques from optimal transportation, Ambrosio's results on transport by BV vector fields and Orlicz spaces. IS - 10 JF - Nonlinearity EP - 2539 TI - Weak stability of Lagrangian solutions to the semigeostrophic equations VL - 22 SP - 2521 KW - semi-geostrophic AU - Faria, Josiane AU - Filho, Milton AU - Lopes, Helena PY - 2009/// UR - http://dx.doi.org/10.1088/0951-7715/22/10/011 ER -