Regularity of solutions for the Boltzmann equation without angular cutoff

Reynaud, Alexandre; Morimoto, Y.; Ukai, Seiji; Xu, Chao-Jiang; Yang, Tong

doi:10.1016/j.crma.2009.04.025

Cited by 8 publications

(20 citation statements)

References 16 publications

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“…In this Note, we shall prove the existence and uniqueness of local classical solutions for the spatially inhomogeneous case so that it complements the regularization result shown in [2]. Let us recall that some solutions have already been constructed in [1,4].…”

Section: Introduction and Main Resultsmentioning

confidence: 76%

“…Let us recall that some solutions have already been constructed in [1,4]. However, they are not sufficient to initialize the regularization properties shown in [2], see also [5] for Gevrey class solutions.…”

Section: Introduction and Main Resultsmentioning

confidence: 97%

“…This Note is a continuation of [2], concerning the nonlinear spatially inhomogeneous and angular non-cutoff Boltzmann equation…”

Section: Introduction and Main Resultsmentioning

confidence: 98%

“…The uniqueness of Theorem 2.1 implies g 1 = g 2 , so that f 1 = f 2 for t ∈ [0, T * ]. The regularizing effect follows from Theorem 1.1 of [2].…”

Section: Proposition 23mentioning

confidence: 99%

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Existence of local solutions for the Boltzmann equation without angular cutoff

Reynaud

Morimoto²,

Ukai³

et al. 2009

Comptes Rendus. Mathématique

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Section: Introduction and Main Resultsmentioning

confidence: 76%

Section: Introduction and Main Resultsmentioning

confidence: 97%

“…This Note is a continuation of [2], concerning the nonlinear spatially inhomogeneous and angular non-cutoff Boltzmann equation…”

Section: Introduction and Main Resultsmentioning

confidence: 98%

“…The uniqueness of Theorem 2.1 implies g 1 = g 2 , so that f 1 = f 2 for t ∈ [0, T * ]. The regularizing effect follows from Theorem 1.1 of [2].…”

Section: Proposition 23mentioning

confidence: 99%

See 2 more Smart Citations

Existence of local solutions for the Boltzmann equation without angular cutoff

Reynaud

Morimoto²,

Ukai³

et al. 2009

Comptes Rendus. Mathématique

Self Cite

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“…And in [3] the following upper bound estimate was proven: for any m, α ∈ R, there exists C > 0 such that…”

Section: Functional Properties Of the Collision Operatormentioning

confidence: 98%

Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff

Reynaud

Morimoto²,

Ukai

et al. 2010

Comptes Rendus. Mathématique

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Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff

Reynaud

Morimoto

Ukai³

et al. 2011

Commun. Math. Phys.

128

150

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Abstract. We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and C ∞ in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem.

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Regularity of solutions for the Boltzmann equation without angular cutoff

Cited by 8 publications

References 16 publications

Existence of local solutions for the Boltzmann equation without angular cutoff

Existence of local solutions for the Boltzmann equation without angular cutoff

Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff

Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff

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