caa a22 4500 60551559X CHVBK 20210128100710.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00205-015-0847-0 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0847-0 A Degenerate Fourth-Order Parabolic Equation Modeling Bose-Einstein Condensation. Part I: Local Existence of Solutions [Elektronische Daten] [Ansgar Jüngel, Michael Winkler] A degenerate fourth-order parabolic equation modeling condensation phenomena related to Bose-Einstein particles is analyzed. The model is a Fokker-Planck-type approximation of the Boltzmann-Nordheim equation, only keeping the leading order term. It maintains some of the main features of the kinetic model, namely mass and energy conservation and condensation at zero energy. The existence of a local-in-time nonnegative continuous weak solution is proven. If the solution is not global, it blows up with respect to the L ∞ norm in finite time. The proof is based on approximation arguments, interpolation inequalities in weighted Sobolev spaces, and suitable a priori estimates for a weighted gradient L 2 norm. Springer-Verlag Berlin Heidelberg, 2015 Jüngel Ansgar Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040, Wien, Austria aut Winkler Michael Institut für Mathematik, Universität Paderborn, 33098, Paderborn, Germany aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 935-973 0003-9527 217:3<935 2015 217 205 https://doi.org/10.1007/s00205-015-0847-0 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/s00205-015-0847-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jüngel Ansgar Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040, Wien, Austria aut NATIONALLICENCE 700 1- Winkler Michael Institut für Mathematik, Universität Paderborn, 33098, Paderborn, Germany aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 935-973 0003-9527 217:3<935 2015 217 205