Abstract
In order to accommodate general initial data, an appropriately relaxed notion of renormalized Lagrangian solutions for the Semi-Geostrophic 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 said stability and approximating solutions with regular initial data. The renormalization property ensures the return from physical to dual space; as consequences we get conservation of Hamiltonian energy and some weak time-regularity of solutions.
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Communicated by D. Kinderlehrer
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Feldman, M., Tudorascu, A. On the Semi-geostrophic System in Physical Space with General Initial Data. Arch Rational Mech Anal 218, 527–551 (2015). https://doi.org/10.1007/s00205-015-0865-y
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DOI: https://doi.org/10.1007/s00205-015-0865-y