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Uniqueness of Bounded Solutions for the Homogeneous Landau Equation with a Coulomb Potential

Abstract : We prove the uniqueness of bounded solutions for the spatially homogeneous Fokker-Planck-Landau equation with a Coulomb potential. Since the local (in time) existence of such solutions has been proved by Arsen'ev-Peskov (Z. Vycisl. Mat. i Mat. Fiz. 17:1063-1068, 1977), we deduce a local well-posedness result. The stability with respect to the initial condition is also checked.
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Submitted on : Tuesday, May 1, 2012 - 7:26:07 PM
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Nicolas Fournier. Uniqueness of Bounded Solutions for the Homogeneous Landau Equation with a Coulomb Potential. Communications in Mathematical Physics, Springer Verlag, 2010, 299 (3), pp.765--782. ⟨10.1007/s00220-010-1113-9⟩. ⟨hal-00693006⟩

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