Weak stability of Lagrangian solutions to the semigeostrophic equations
Weak stability of Lagrangian solutions to the semigeostrophic equations
复制标题
半地转方程拉格朗日解的弱稳定性
DOI：
10.1088/0951-7715/22/10/011
复制
发表时间：
2009
期刊：
影响因子：
1.7
通讯作者：
H. J. Nussenzveig Lopes
中科院分区：
文献类型：
--
作者：
J. Faria;M. C. Lopes Filho;H. J. Nussenzveig Lopes
在（Cullen and Feldman 2006 SIAM J. Math. Anal. 37 137–95）中，Cullen 和 Feldman 证明了半地转系统的拉格朗日解存在于初始位涡为 Lp，p > 1 的物理变量中。这里，我们证明了与 L1 中初始位涡的强收敛序列相对应的拉格朗日解的子序列在Lq, q < Infini, 到拉格朗日解，特别是将 Cullen 和 Feldman 的存在结果扩展到 p = 1 的情况。我们还提出了对应于收敛于 的初始位涡序列的拉格朗日解的反例。使用的分析工具包括最优传输技术、Ambrosio 通过 BV 矢量场和 Orlicz 空间得出的传输结果。
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.