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This article is cited in 2 scientific papers (total in 2 papers)
Research Papers
Lagrangian solutions for the semi-geostrophic shallow water system in physical space with general initial data
M. Feldmana, A. Tudorascub a Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706
b Department of Mathematics, West Virginia University, Morgantown, WV 26506
Abstract:
In order to accommodate general initial data, an appropriately relaxed notion of renormalized Lagrangian solutions for the Semi-Geostrophic Shallow Water system in physical space is introduced. This is shown to be consistent with previous notions, generalizing them. A weak stability result is obtained first, followed by a general existence result whose proof employs the said stability and approximating solutions with regular initial data. The renormalization property ensures the return from physical to dual space and ultimately enables us to achieve the desired results.
Keywords:
Semi-Geostrophic Shallow Water system, flows of maps, optimal mass transport, Wasserstein metric, optimal maps, absolutely continuous curves.
Received: 25.11.2014
Citation:
M. Feldman, A. Tudorascu, “Lagrangian solutions for the semi-geostrophic shallow water system in physical space with general initial data”, Algebra i Analiz, 27:3 (2015), 272–300; St. Petersburg Math. J., 27:3 (2016), 547–568
Linking options:
https://www.mathnet.ru/eng/aa1444 https://www.mathnet.ru/eng/aa/v27/i3/p272
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