Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation

DOI10.1016/j.aim.2021.108159zbMath1481.35303arXiv2105.00474OpenAlexW3159642874MaRDI QIDQ2065956

Lvqiao Liu, Wei-Xi Li, Renjun Duan

Publication date: 13 January 2022

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.00474

zbMATH Keywords

Boltzmann equationsymbolic calculusGevrey regularitynon-cutoffhypoelliptic estimate

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Perturbations in context of PDEs (35B20) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Hypoelliptic equations (35H10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Boltzmann equations (35Q20)

Related Items (6)

Propagation of Gevrey regularity for solution of non-cutoff Boltzmann equation ⋮ Global existence of non-cutoff Boltzmann equation in weighted Sobolev space ⋮ Analytic smoothing effect of the spatially inhomogeneous Landau equations for hard potentials ⋮ The Gevrey regularity for the Vlasov-Poisson-Landau and the non-cutoff Vlasov-Poisson-Boltzmann systems ⋮ The smoothing effect in sharp Gevrey space for the spatially homogeneous non-cutoff Boltzmann equations with a hard potential ⋮ Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential

Cites Work

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• Sharp regularity properties for the non-cutoff spatially homogeneous Boltzmann equation
• Global well-posedness in spatially critical Besov space for the Boltzmann equation
• Cauchy problem and exponential stability for the inhomogeneous Landau equation
• Global solutions in the critical Besov space for the non-cutoff Boltzmann equation
• A new regularization mechanism for the Boltzmann equation without cut-off
• Regularity of the Boltzmann equation in convex domains
• Global well-posedness of the Boltzmann equation with large amplitude initial data
• Global existence and full regularity of the Boltzmann equation without angular cutoff
• Energy method for Boltzmann equation
• Gevrey smoothing effect of solutions for spatially homogeneous nonlinear Boltzmann equation without angular cutoff
• 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
• Decay and continuity of the Boltzmann equation in bounded domains
• Regularizing effect and local existence for the non-cutoff Boltzmann equation
• An \(L^2\) to \(L^\infty\) framework for the Landau equation
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• Uncertainty principle and kinetic equations
• Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff
• Ultra-analytic effect of Cauchy problem for a class of kinetic equations
• Analytic smoothness effect of solutions for spatially homogeneous Landau equation
• Boltzmann equation: micro-macro decompositions and positivity of shock profiles
• Entropy dissipation and long-range interactions
• Landau equation for very soft and Coulomb potentials near maxwellians
• Solution to the Boltzmann equation in velocity-weighted Chemin-Lerner type spaces
• The Landau equation in a periodic box
• About the regularizing properties of the non-cut-off Kac equation
• The Landau equation with the specular reflection boundary condition
• Non-cutoff Boltzmann equation with polynomial decay perturbations
• The Cauchy problem for the radially symmetric homogeneous Boltzmann equation with Shubin class initial datum and Gelfand-Shilov smoothing effect
• Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules
• The Schauder estimate for kinetic integral equations
• Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off
• Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules
• The weak Harnack inequality for the Boltzmann equation without cut-off
• Decay estimates for large velocities in the Boltzmann equation without cutoff
• Gelfand-Shilov smoothing properties of the radially symmetric spatially homogeneous Boltzmann equation without angular cutoff
• Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff
• Local existence with mild regularity for the Boltzmann equation
• 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
• Gevrey Hypoellipticity for a Class of Kinetic Equations
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules
• Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation
• On the Boltzmann equation for long-range interactions
• The Boltzmann equation in the whole space
• Global Mild Solutions of the Landau and <scp>Non‐Cutoff</scp> Boltzmann Equations
• Global hypoelliptic estimates for fractional order kinetic equation
• THE BOLTZMANN EQUATION IN THE SPACE $L^2\cap L^\infty_\beta$: GLOBAL AND TIME-PERIODIC SOLUTIONS

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