On Lagrangian Solutions for the Semi-geostrophic System with Singular Initial Data
On Lagrangian Solutions for the Semi-geostrophic System with Singular Initial Data
复制标题
具有奇异初始数据的半地转系统的拉格朗日解
DOI：
10.1137/120870116
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
A. Tudorascu
中科院分区：
文献类型：
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作者：
M. Feldman;A. Tudorascu
我们证明了物理空间中具有一定时间规律性的半地转系统的弱(欧拉解)解不能在对偶空间中产生点质量。然而，这样的解决方案与模型在物理上是相关的。因此，我们讨论了物理空间中弱拉格朗日解的自然推广，以包含对偶空间中奇异测度的可能性。我们证明了在对偶空间中离散测度的情况下解的存在性。证明了物理空间中的弱拉格朗日解决定了对偶空间中的解。这意味着在物理空间中沿拉格朗日轨迹的地转能量守恒。
We show that weak (Eulerian) solutions for the semi-geostrophic system in physical space exhibiting some mild regularity in time cannot yield point masses in dual space. However, such solutions are physically relevant to the model. Thus, we discuss a natural generalization of weak Lagrangian solutions in the physical space to include the possibility of singular measures in dual space. We prove existence of such solutions in the case of discrete measures in dual space. We also prove that weak Lagrangian solutions in physical space determine solutions in the dual space. This implies conservation of geostrophic energy along the Lagrangian trajectories in the physical space.