Propagation of regularity and long time behavior of $3D$ massive relativistic transport equation I: Vlasov-Nordström system

Wang, Xuecheng

doi:10.48550/arxiv.1804.06560

Cited by 6 publications

(24 citation statements)

References 36 publications

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“…In particular, this allows to clarify the role of some of the assumptions and to isolate a particularly simple asymptotic dynamic. We hope that this framework will be useful when considering coupling of kinetic equations and other (particularly dispersive) equations (see [19,20] for examples of such problems). 1.2.…”

mentioning

confidence: 99%

On the asymptotic behavior of solutions to the Vlasov-Poisson system

Ionescu¹,

Pausader²,

Wang³

et al. 2020

Preprint

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mentioning

confidence: 99%

On the asymptotic behavior of solutions to the Vlasov-Poisson system

Ionescu¹,

Pausader²,

Wang³

et al. 2020

Preprint

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“…In particular, the stability of vacuum has been established in many different settings [21,39,83,102], and the stability of the Minkowski spacetime for the Einstein-Vlasov system in general relativity has also been resolved [22,38,68,84,91]. (See also [5,4,44,41,98,97,96] for related works on stability of vacuum type results for collisionless models.) For collisional models, recent works using the commutating vector field method give -for the first time -stability of vacuum results for collisional models with a long range interaction, first for the Landau equation [69,29], and more recently for Boltzmann equation without angular cutoff [28].…”

Section: 21mentioning

confidence: 99%

The Vlasov--Poisson--Landau system in the weakly collisional regime

Chaturvedi¹,

Luk²,

Nguyen³

2021

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Consider the Vlasov-Poisson-Landau system with Coulomb potential in the weakly collisional regime on a 3-torus, i.e.with ν ≪ 1. We prove that for ǫ > 0 sufficiently small (but independent of ν), initial data which are O(ǫν 1 3 )-Sobolev space perturbations from the global Maxwellians lead to globalin-time solutions which converge to the global Maxwellians as t → ∞. The solutions exhibit uniform-in-ν Landau damping and enhanced dissipation.Our main result is analogous to an earlier result of Bedrossian for the Vlasov-Poisson-Fokker-Planck equation with the same threshold. However, unlike in the Fokker-Planck case, the linear operator cannot be inverted explicitly due to the complexity of the Landau collision operator. For this reason, we develop an energy-based framework, which combines Guo's weighted energy method with the hypocoercive energy method and the commuting vector field method. The proof also relies on pointwise resolvent estimates for the linearized density equation.

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“…Relations between these results and the stability of vacuum for the Boltzmann equation with angular cutoff is discussed in [10]. More recent results can be found in [13,14,15,16,17,24,50,64,65,63,66]. See also [23,46,56] for proof of the stability of the Minkowski spacetime for the Einstein-Vlasov system.…”

Section: Introductionmentioning

confidence: 99%

Stability of vacuum for the Landau equation with hard potentials

Chaturvedi

2020

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We consider the spatially inhomogeneous Landau equation with Maxwellian and hard potentials (i.e with γ ∈ [0, 1)) on the whole space R 3 . We prove that if the initial data f in are close to the vacuum solution f vac = 0 in an appropriate weighted norm then the solution f exists globally in time. This work builds up on the author's earlier work on local existence of solutions to Landau equation with hard potentials.Our proof uses L 2 estimates and exploits the null-structure established by Luk [Stability of vacuum for the Landau equation with moderately soft potentials, Annals of PDE (2019) 5:11]. To be able to close our estimates, we have to couple the weighted energy estimates, which were established by the author in a previous paper [Local existence for the Landau equation with hard potentials, https://arxiv.org/abs/1910.11866], with the null-structure and devise new weighted norms that take this into account.

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Propagation of regularity and long time behavior of $3D$ massive relativistic transport equation I: Vlasov-Nordström system

Cited by 6 publications

References 36 publications

On the asymptotic behavior of solutions to the Vlasov-Poisson system

On the asymptotic behavior of solutions to the Vlasov-Poisson system

The Vlasov--Poisson--Landau system in the weakly collisional regime

Stability of vacuum for the Landau equation with hard potentials

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