Mathematics – Analysis of PDEs
Scientific paper
2009-01-25
Nonlinearity 22 (2009), 2521-2539
Mathematics
Analysis of PDEs
19 pages
Scientific paper
10.1088/0951-7715/22/10/011
In [1], Cullen and Feldman proved 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 $L^q$, $q<\infty$, 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. [1] M. Cullen and M. Feldman, {\it Lagrangian solutions of semigeostrophic equations in physical space.} SIAM J. Math. Anal., {\bf 37} (2006), 1371--1395.
Faria Josiane C. O.
Lopes Filho Milton C.
Nussenzveig Lopes Helena J.
No associations
LandOfFree
Weak stability of Lagrangian solutions to the semigeostrophic equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Weak stability of Lagrangian solutions to the semigeostrophic equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak stability of Lagrangian solutions to the semigeostrophic equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-504177