Abstract
A global existence theorem with large initial data inL 1 is given for the modified Enskog equation in ℝ3. The method, which is based on the existence of a Liapunov functional (analog of theH-Boltzmann theorem), utilizes a weak compactness argument inL 1 in a similar way to the DiPerna-Lions proof for the Boltzmann equation. The existence theorem is obtained under certain condition on the behavior of the geometric factorY. The condition onY amounts to the fact that theL 1 norm of the collision term grows linearly when the local density tends to infinity.
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Polewczak, J. Global existence inL 1 for the modified nonlinear Enskog equation in ℝ3 . J Stat Phys 56, 159–173 (1989). https://doi.org/10.1007/BF01044239
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DOI: https://doi.org/10.1007/BF01044239