2020
DOI: 10.48550/arxiv.2011.01503
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The Boltzmann equation with large-amplitude initial data and specular reflection boundary condition

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Cited by 5 publications
(6 citation statements)
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“…By defining mild solution, low regularity L ∞ solutions have been studied after [12]. There are lots of references [2,4,5,6,8,18,19,22,23], where the low regularity solutions were studied for the cut-off type Boltzmann equation. We also refer to recent results [1,7,13,21], etc., which deal with low regularity solution of the kinetic equation whose collision operator have regularizing effect such as non-cutoff Boltzmann or Landau equation.…”
Section: Introductionmentioning
confidence: 99%
“…By defining mild solution, low regularity L ∞ solutions have been studied after [12]. There are lots of references [2,4,5,6,8,18,19,22,23], where the low regularity solutions were studied for the cut-off type Boltzmann equation. We also refer to recent results [1,7,13,21], etc., which deal with low regularity solution of the kinetic equation whose collision operator have regularizing effect such as non-cutoff Boltzmann or Landau equation.…”
Section: Introductionmentioning
confidence: 99%
“…x,v data. And recently, combining with idead of [25], the large amplitude problem with specular reflection in C 3 convex domain with small relative entropy (1.7) has been resolved in [14].…”
Section: Introductionmentioning
confidence: 99%
“…(Lemma 2.4.) Unlike to hard potential case ( [13], [14]), however, Γ − can be treated in another way. Nonlinear Γ − contains local term f (v), so we see factor v γ .…”
Section: Introductionmentioning
confidence: 99%
“…In the end, we also mention extensive studies of the conditional regularity of solutions to the spatially inhomogeneous Boltzmann equation for general initial data in [39][40][41][42]56] by Silvestre together with his collaborators. It would be interesting to develop a self-contained theory of both existence and regularity without any extra condition on solutions to the spatially inhomogeneous non-cutoff Boltzmann equation with initial data allowing to have possibly large oscillations in space variable, for instance, see [22,23] in the cutoff case where the L ∞ norm can be arbitrarily large but the relative entropy is small enough. 1.4.…”
Section: Introductionmentioning
confidence: 99%