Explicit coercivity estimates for the linearized Boltzmann and Landau operators
نویسنده
چکیده
We prove explicit coercivity estimates for the linearized Boltzmann and Landau operators, for a general class of interactions including any inversepower law interactions, and hard spheres. The functional spaces of these coecivity estimates depend on the collision kernel of these operators. For Maxwell molecules they coincide with the spectral gap estimates. For hard potentials they are stronger and imply these spectral estimates. For soft potentials, they play the role of explicit “degenerated spectral gap” estimates. The proofs are based on the reduction to the Maxwell case by decomposition methods. We also prove a regularity property for the linearized Boltzmann operator for non locally integrable collision kernel and for the linearized Landau operator, and we discuss the consequence on its spectrum. Mathematics Subject Classification (2000): 76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05].
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