Explicit Coercivity Estimates for the Linearized Boltzmann and Landau Operators

By Clément Mouhot. 2006

133 citations recorded by the source corpus.

We prove explicit coercivity estimates for the linearized Boltzmann and Landau operators, for a general class of interactions including any inverse-power law interactions, and hard spheres. The functional spaces of these coercivity estimates depend on the collision kernel of these operators. They cover the spectral gap estimates for the linearized Boltzmann operator with Maxwell molecules, improve these estimates for hard potentials, and are the first explicit coercivity estimates for soft potentials (including in particular the case of Coulombian interactions). We also prove a regularity property for the linearized Boltzmann operator with non locally integrable collision kernels, and we deduce from it a new proof of the compactness of its resolvent for hard potentials without angular cutoff.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/06691aa2ce823b97212471dc6350e8973babfcce

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Factorization for non-symmetric operators and exponential H-theorem (2010, methodology): “erator has a spectral gap [79, 48] and we expect our factorization method to be applicable in this case by using a dierent decomposition of the linearized collision operator, such as the one used in [74] in order to quantify the spectral gap in velocity only. In the case of very soft potentials, the”
Global classical solutions of the Boltzmann equation without angular cut-off (2009, methodology): “diﬀerential operators. And they sharpen some of the isotropic coercivity and upper bound estimates for the Boltzmann collision operator. We also mention the linear isotropic coercivity estimates from [67,68]. In particular Mouhot-Strain [68] proved the coercive lower bound for the linearized collisi”
The Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential (2010, result): “Since it is known from [31] that we have ( Lg, g ) L2 ≥ C‖(I − P)g‖(2) L2 γ/2 ,”
Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff (2009, methodology): “[41] P.-T. Gressman and R.-M. Strain, Global strong solutions f the Boltzmann equation without cutoff. http://www.math.upenn.edu/∼strain/preprints/0912.0888.pdf, 2009.”