caa a22 4500 605515514 CHVBK 20210128100709.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00205-015-0852-3 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0852-3 Existence of Compactly Supported Global Minimisers for the Interaction Energy [Elektronische Daten] [José Cañizo, José Carrillo, Francesco Patacchini] The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not H-stable, which is the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics. The proof is based on a uniform control on the local mass around each point of the support of a global minimiser, together with an estimate on the size of the "gaps" it may have. The class of potentials for which we prove the existence of global minimisers includes power-law potentials and, for some range of parameters, Morse potentials, widely used in applications. We also show that the support of local minimisers is compact under suitable assumptions. The Author(s), 2015 Cañizo José School of Mathematics, Watson Building, University of Birmingham, Edgbaston, B152TT, Birmingham, UK aut Carrillo José Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London, UK aut Patacchini Francesco Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London, UK aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 1197-1217 0003-9527 217:3<1197 2015 217 205 https://doi.org/10.1007/s00205-015-0852-3 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/s00205-015-0852-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cañizo José School of Mathematics, Watson Building, University of Birmingham, Edgbaston, B152TT, Birmingham, UK aut NATIONALLICENCE 700 1- Carrillo José Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London, UK aut NATIONALLICENCE 700 1- Patacchini Francesco Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, London, UK aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 1197-1217 0003-9527 217:3<1197 2015 217 205