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Results 1 - 10
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279
Explicit coercivity estimates for the linearized Boltzmann and Landau operators
- Comm. Partial Diff. Eq
"... Abstract. 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. ..."
Abstract
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Cited by 28 (3 self)
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Abstract. 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
Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials
, 2003
"... We prove explicit spectral gap estimates for the linearized Boltzmann operator with hard potentials (and hard spheres). We prove that it can reduce to the Maxwellian case, for which explicit estimates are already known. The method is constructive, does not rely on Weyl's Theorem and thus doe ..."
Abstract
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Cited by 31 (10 self)
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We prove explicit spectral gap estimates for the linearized Boltzmann operator with hard potentials (and hard spheres). We prove that it can reduce to the Maxwellian case, for which explicit estimates are already known. The method is constructive, does not rely on Weyl's Theorem and thus
PHASE SPACE ANALYSIS AND FUNCTIONAL CALCULUS FOR THE LINEARIZED LANDAU AND BOLTZMANN OPERATORS
"... doi:10.3934/xx.xx.xx.xx pp. X–XX ..."
Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators
"... ..."
Linearized quantum and relativistic Fokker-Planck-Landau equations
, 2000
"... After a recent work on spectral properties and dispersion relations of the linearized classical Fokker-Planck-Landau operator [8], we establish in this paper analogous results for two more realistic collision operators: The first one is the Fokker-Planck-Landau collision operator obtained by relativ ..."
Abstract
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Cited by 10 (0 self)
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by relativistic calculations of binary interactions, and the second is a collision operator (of Fokker-Planck-Landau type) derived from the Boltzmann operator in which quantum effects have been taken into account. We apply Sobolev-Poincar'e inequalities to establish the spectral gap of the linearized
On the Spectrum of the Linear Boltzmann Operator
, 1996
"... The continuous spectrum of the linear Boltzmann operator with constant field is derived. It is found that a sufficiency relation for runaway phenomena is consistent with another sufficiency relation for the hydrodynamic regime to exist. There is a further class of systems whose behaviour lies in ..."
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The continuous spectrum of the linear Boltzmann operator with constant field is derived. It is found that a sufficiency relation for runaway phenomena is consistent with another sufficiency relation for the hydrodynamic regime to exist. There is a further class of systems whose behaviour lies
Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff
- J. Math. Pures Appl
"... Abstract. In this paper we prove new constructive coercivity estimates for the Boltzmann collision operator without cutoff, that is for long-range interactions. In particular we give a generalized sufficient condition for the existence of a spectral gap which involves both the growth behavior of the ..."
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Cited by 32 (2 self)
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] and we formulate a conjecture about a unified necessary and sufficient condition for the existence of a spectral gap for Boltzmann and Landau linearized collision operators.
Results 1 - 10
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279
