LOCAL IN TIME SOLUTION TO ES-BGK MODEL WITH CORRECT PRANDTL NUMBER

Sung Jun Son; Seok Bae Yun

doi:10.3934/krm.2024024

LOCAL IN TIME SOLUTION TO ES-BGK MODEL WITH CORRECT PRANDTL NUMBER

Sung Jun Son
, Seok Bae Yun

Department of Mathematics

Pohang University of Science and Technology

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the existence of a unique mild solution for the ellipsoidal BGK model with the critical Prandtl parameter ν = −1/2. The key difficulty is the breakdown of the equivalence between the local temperature and the temperature tensor in this critical case. To overcome this, we use the fact that the quadratic polynomial of the temperature tensor can be written as the difference of the directional temperatures, which enables us to control the temperature tensor from below for a finite time.

Original language	English
Pages (from-to)	499-519
Number of pages	21
Journal	Kinetic and Related Models
Volume	18
Issue number	4
DOIs	https://doi.org/10.3934/krm.2024024
State	Published - 2025

Keywords

BGK model
Boltzmann equation
Cauchy problem
correct Prandtl number
ellipsoidal BGK model
Kinetic theory of gases

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10.3934/krm.2024024

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title = "LOCAL IN TIME SOLUTION TO ES-BGK MODEL WITH CORRECT PRANDTL NUMBER",

abstract = "In this paper, we study the existence of a unique mild solution for the ellipsoidal BGK model with the critical Prandtl parameter ν = −1/2. The key difficulty is the breakdown of the equivalence between the local temperature and the temperature tensor in this critical case. To overcome this, we use the fact that the quadratic polynomial of the temperature tensor can be written as the difference of the directional temperatures, which enables us to control the temperature tensor from below for a finite time.",

keywords = "BGK model, Boltzmann equation, Cauchy problem, correct Prandtl number, ellipsoidal BGK model, Kinetic theory of gases",

author = "Son, \{Sung Jun\} and Yun, \{Seok Bae\}",

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journal = "Kinetic and Related Models",

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publisher = "American Institute of Mathematical Sciences",

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AU - Son, Sung Jun

AU - Yun, Seok Bae

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N2 - In this paper, we study the existence of a unique mild solution for the ellipsoidal BGK model with the critical Prandtl parameter ν = −1/2. The key difficulty is the breakdown of the equivalence between the local temperature and the temperature tensor in this critical case. To overcome this, we use the fact that the quadratic polynomial of the temperature tensor can be written as the difference of the directional temperatures, which enables us to control the temperature tensor from below for a finite time.

AB - In this paper, we study the existence of a unique mild solution for the ellipsoidal BGK model with the critical Prandtl parameter ν = −1/2. The key difficulty is the breakdown of the equivalence between the local temperature and the temperature tensor in this critical case. To overcome this, we use the fact that the quadratic polynomial of the temperature tensor can be written as the difference of the directional temperatures, which enables us to control the temperature tensor from below for a finite time.

KW - BGK model

KW - Boltzmann equation

KW - Cauchy problem

KW - correct Prandtl number

KW - ellipsoidal BGK model

KW - Kinetic theory of gases

UR - https://www.scopus.com/pages/publications/105007818964

U2 - 10.3934/krm.2024024

DO - 10.3934/krm.2024024

M3 - Article

AN - SCOPUS:105007818964

SN - 1937-5093

VL - 18

SP - 499

EP - 519

JO - Kinetic and Related Models

JF - Kinetic and Related Models

IS - 4

ER -

LOCAL IN TIME SOLUTION TO ES-BGK MODEL WITH CORRECT PRANDTL NUMBER

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Keywords

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