A Degenerate Fourth-Order Parabolic Equation Modeling Bose–Einstein Condensation. Part I: Local Existence of Solutions

被引：0
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作者：
Ansgar Jüngel
Michael Winkler
机构：
[1] Vienna University of Technology,Institute for Analysis and Scientific Computing
[2] Universität Paderborn,Institut für Mathematik
来源：
Archive for Rational Mechanics and Analysis | 2015年 / 217卷
关键词：
Einstein Condensation; Local Existence; Weighted Sobolev Space; Interpolation Inequality; Approximate Problem;
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摘要：
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 L2 norm.
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页码：935 / 973
页数：38
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