Macroscopic regularity for the Boltzmann equation

DOI10.1016/S0252-9602(18)30831-2zbMath1438.35304arXiv1512.08608OpenAlexW2963068083MaRDI QIDQ2313158

Yong Wang, Fei-Min Huang

Publication date: 18 July 2019

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.08608

zbMATH Keywords

Boltzmann equationcompressible Navier-Stokes equationsmacroscopic regularity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Boltzmann equations (35Q20)

Related Items

Global weak solutions for a nonlinear hyperbolic system ⋮ Global well-posedness of the Boltzmann equation with large amplitude initial data

Cites Work

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• Smoothing effect of weak solutions for the spatially homogeneous Boltzmann equation without angular cutoff
• Global solutions of the Boltzmann equation over \({\mathbb{R}^D}\) near global Maxwellians with small mass
• Global well-posedness of the Boltzmann equation with large amplitude initial data
• Formation and propagation of discontinuity for Boltzmann equation in non-convex domains
• Regularizing effect and local existence for the non-cutoff Boltzmann equation
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• On the Cauchy problem for the Boltzmann equation in the whole space: Global existence and uniform stability in \(L_{\xi}^{2}(H_{x}^{N})\)
• Propagation of singularities for classical solutions of the Vlasov-Poisson-Boltzmann equation
• Regularity of the moments of the solution of a transport equation
• Global solutions to the initial value problem for the nonlinear Boltzmann equation
• The Boltzmann equation. I. Uniqueness and local existence
• Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas
• The mathematical theory of dilute gases
• Regularity theory for the spatially homogeneous Boltzmann equation with cut-off
• On the singularities of the global small solutions of the full Boltzmann equation
• Classical solution of the nonlinear Boltzmann equation in all \({\mathbb{R}}^ 3\): asymptotic behavior of solutions.
• A new characterization and global regularity of infinite energy solutions to the homogeneous Boltzmann equation
• Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff
• PROPAGATION OF SINGULARITIES IN THE SOLUTIONS TO THE BOLTZMANN EQUATION NEAR EQUILIBRIUM
• Infinite energy solutions to the homogeneous Boltzmann equation
• Existence in the large and asymptotic behaviour for the Boltzmann equation
• A NOTE ON THE PROPAGATION OF BOUNDARY INDUCED DISCONTINUITIES IN KINETIC THEORY
• The Boltzmann equation in the whole space
• On the Cauchy problem for the nonlinear Boltzmann equation global existence uniqueness and asymptotic stability
• Bounded solutions for the Boltzmann equation
• THE BOLTZMANN EQUATION IN THE SPACE $L^2\cap L^\infty_\beta$: GLOBAL AND TIME-PERIODIC SOLUTIONS