The large amplitude solution of the Boltzmann equation with soft potential

Ko, Gyounghun; Lee, Dong-Hyun; Park, Kwanghyuk

doi:10.1016/j.jde.2021.10.041

Cited by 4 publications

(2 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Lastly, we note that the

L^2-L^\infty

method established in [17, 23] has been widely used to various problems, such as global well‐posedness with large amplitude external potential ([20]), rotational setting [21], and large amplitude problem with smooth convex domain [10]. We also refer recent global well‐posedness results with large amplitude initial data for various setting [8, 9, 11, 26].…”

Section: Introductionmentioning

confidence: 99%

Hölder regularity of the Boltzmann equation past an obstacle

Kim,

Lee

2023

Comm Pure Appl Math

Self Cite

View full text Add to dashboard Cite

Regularity and singularity of the solutions according to the shape of domains is a challenging research theme in the Boltzmann theory. In this paper, we prove an Hölder regularity in for the Boltzmann equation of the hard‐sphere molecule, which undergoes the elastic reflection in the intermolecular collision and the contact with the boundary of a convex obstacle. In particular, this Hölder regularity result is a stark contrast to the case of other physical boundary conditions (such as the diffuse reflection boundary condition and in‐flow boundary condition), for which the solutions of the Boltzmann equation develop discontinuity in a codimension 1 subset (Kim [Comm. Math. Phys. 308 (2011)]), and therefore the best possible regularity is BV, which has been proved by Guo et al. [Arch. Rational Mech. Anal. 220 (2016)].

show abstract

“…Lastly, we note that the

L^2-L^\infty

Section: Introductionmentioning

confidence: 99%

Hölder regularity of the Boltzmann equation past an obstacle

Kim,

Lee

2023

Comm Pure Appl Math

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently, authors in [23] provide new analysis to derive L ∞ estimate rather than using Green function and Duhamel's principle. In addition, there are lots of references [2,4,5,6,8,18,19,22,24], where the low regularity solutions were studied for the cut-off type Boltzmann equation. We also refer to recent results [1,7,14,21], etc., which deal with low regularity solution of the kinetic equation whose collision operator has regularizing effect such as non-cutoff Boltzmann or Landau equation.…”

mentioning

confidence: 99%

On <inline-formula><tex-math id="M1">$ C^{2} $</tex-math></inline-formula> solution of the free-transport equation in a disk

Lee

2023

KRM

View full text Add to dashboard Cite

<p style='text-indent:20px;'>The free transport operator of probability density function <inline-formula><tex-math id="M2">\begin{document}$ f(t, x, v) $\end{document}</tex-math></inline-formula> is one the most fundamental operator which is widely used in many areas of PDE theory including kinetic theory, in particular. When it comes to general boundary problems in kinetic theory, however, it is well-known that high order regularity is very hard to obtain in general. In this paper, we study the free transport equation in a disk with the specular reflection boundary condition. We obtain initial-boundary compatibility conditions for <inline-formula><tex-math id="M3">\begin{document}$ C^{1}_{t, x, v} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ C^{2}_{t, x, v} $\end{document}</tex-math></inline-formula> regularity of the solution. We also provide regularity estimates.</p>

show abstract

Hölder regularity of the Boltzmann equation in some non-convex domains

Lee,

Kim

2024

AIP Conference Proceedings

View full text Add to dashboard Cite

The large amplitude solution of the Boltzmann equation with soft potential

Cited by 4 publications

References 26 publications

Hölder regularity of the Boltzmann equation past an obstacle

Hölder regularity of the Boltzmann equation past an obstacle

On <inline-formula><tex-math id="M1">$ C^{2} $</tex-math></inline-formula> solution of the free-transport equation in a disk

Hölder regularity of the Boltzmann equation in some non-convex domains

Contact Info

Product

Resources

About