caa a22 4500 605515719 CHVBK 20210128100710.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00205-015-0865-y doi (NATIONALLICENCE)springer-10.1007/s00205-015-0865-y On the Semi-geostrophic System in Physical Space with General Initial Data [Elektronische Daten] [Mikhail Feldman, Adrian Tudorascu] 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. Springer-Verlag Berlin Heidelberg, 2015 Feldman Mikhail Department of Mathematics, University of Wisconsin-Madison, 53706, Madison, WI, USA aut Tudorascu Adrian Department of Mathematics, West Virginia University, 26506, Morgantown, WV, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/1(2015-10-01), 527-551 0003-9527 218:1<527 2015 218 205 https://doi.org/10.1007/s00205-015-0865-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0865-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Feldman Mikhail Department of Mathematics, University of Wisconsin-Madison, 53706, Madison, WI, USA aut NATIONALLICENCE 700 1- Tudorascu Adrian Department of Mathematics, West Virginia University, 26506, Morgantown, WV, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/1(2015-10-01), 527-551 0003-9527 218:1<527 2015 218 205