A. Jüngel, M. Winkler:

"A degenerate fourth-order parabolic equation modeling Bose-Einstein condensation. Part I: Local existence of solutions";

in: "ASC Report 5/2014", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 35.

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 L1 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 L2 norm.

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 main

http://www.asc.tuwien.ac.at/preprint/2014/asc05x2014.pdf

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