Global solutions in the critical Besov space for the non-cutoff Boltzmann equation

DOI10.1016/j.jde.2016.06.017zbMath1358.35081arXiv1512.00585OpenAlexW2963158010MaRDI QIDQ305425

Yoshinori Morimoto, Shota Sakamoto

Publication date: 29 August 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.00585

zbMATH Keywords

global solutionBoltzmann equationcritical Besov spaceno angular cut-offtriple norm

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Boltzmann equations (35Q20)

Related Items (12)

De Giorgi argument for weighted \(L^2\cap L^{\infty}\) solutions to the non-cutoff Boltzmann equation ⋮ The Fokker–Planck–Boltzmann equation in the finite channel ⋮ Global well-posedness of the quantum Boltzmann equation for bosons interacting via inverse power law potentials ⋮ An \(\boldsymbol{L^1_{k}\cap L^{p}_{k}}\) Approach for the Non-Cutoff Boltzmann Equation in \(\boldsymbol{\mathbb{R}^3}\) ⋮ The Boltzmann equation with large-amplitude initial data in bounded domains ⋮ Solution to the Boltzmann equation in velocity-weighted Chemin-Lerner type spaces ⋮ The Cauchy problem for the inhomogeneous non-cutoff Kac equation in critical Besov space ⋮ Non-cutoff Boltzmann equation with polynomial decay perturbations ⋮ Decay of the Boltzmann equation in spatial critical Besov space ⋮ Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation ⋮ Gelfand-Shilov and Gevrey smoothing effect of the Cauchy problem for Fokker-Planck equation ⋮ Asymptotic stability of the relativistic Boltzmann equation without angular cut-off

Cites Work

• Unnamed Item
• Unnamed Item
• Global well-posedness in spatially critical Besov space for the Boltzmann equation
• Smoothing effect of weak solutions for the spatially homogeneous Boltzmann equation without angular cutoff
• Global existence and full regularity of the Boltzmann equation without angular cutoff
• Energy method for Boltzmann equation
• The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential
• The Boltzmann equation without angular cutoff in the whole space: qualitative properties of solutions
• Regularizing effect and local existence for the non-cutoff Boltzmann equation
• On the Cauchy problem of the Boltzmann equation with a soft potential
• On the Cauchy problem for the Boltzmann equation in Chemin-Lerner type spaces
• Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff
• Global solutions to the initial value problem for the nonlinear Boltzmann equation
• Boltzmann equation: micro-macro decompositions and positivity of shock profiles
• Entropy dissipation and long-range interactions
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations
• Global classical solutions for partially dissipative hyperbolic system of balance laws
• Local existence with mild regularity for the Boltzmann equation
• A new approach to velocity averaging lemmas in Besov spaces
• The Boltzmann equation, Besov spaces, and optimal time decay rates in \(\mathbb{R}_x^n\)
• THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL
• Global classical solutions of the Boltzmann equation without angular cut-off
• Fourier Analysis and Nonlinear Partial Differential Equations
• Integral estimates for a linear singular operator linked with the Boltzmann operator: Part I: Small singularities $0 less than u less than 1$
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• The Boltzmann equation in the whole space

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