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We obtain the existence and uniqueness of L p -solutions (1 p ~) for Fokker-Planck equations with irregular and degenerate coefficients. Moreover, as an application, we also derive the existence and uniqueness of L 1 -solutions for the Fokker-Planck-Boltzmann equation.
The Cauchy problem for the BGK equation with two kinds of force fields is studied in this paper. The first one considers a given force field F(t,x,v) which is assumed to be divergence free with respect to the velocity variable and has an L p integrability. It is shown that there exists a nonnegative distributional solution which extends a previous result obtained by the authors. The second...
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