Spectral gap formation to kinetic equations with soft potentials in bounded domain

DOI10.1007/s00220-022-04519-2OpenAlexW4287186290MaRDI QIDQ2684877

Dingqun Deng, Renjun Duan

Publication date: 17 February 2023

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.00901

zbMATH Keywords

Boltzmann equationspectral gapkinetic equationsLandau equation

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Boltzmann equations (35Q20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On some properties of the Landau kinetic equation
• Spectrum analysis of some kinetic equations
• The initial boundary value problem for the Boltzmann equation with soft potential
• Energy method for Boltzmann equation
• The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential
• Decay and continuity of the Boltzmann equation in bounded domains
• On the Cauchy problem of the Boltzmann equation with a soft potential
• Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• The Boltzmann equation with a soft potential. I: Linear, spatially- homogeneous
• The Boltzmann equation with a soft potential. II: Nonlinear, spatially- periodic
• Classes of linear operators. Vol. I
• The Boltzmann equation and its applications
• Dispersion relations for the linearized Fokker-Planck equation
• Hypoelliptic regularity in kinetic equations.
• Classical solutions to the Boltzmann equation for molecules with an angular cutoff
• 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
• The first and second fluid approximation to the linearized Boltzmann equation
• The Landau equation in a periodic box
• The Landau equation with the specular reflection boundary condition
• Non-cutoff Boltzmann equation with polynomial decay perturbations
• Effects of soft interaction and non-isothermal boundary upon long-time dynamics of rarefied gas
• On the rate of relaxation for the Landau kinetic equation and related models
• Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff
• Exponential decay for soft potentials near Maxwellian
• Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials
• The Vlasov-Poisson-Landau system in \(\mathbb{R}^{3}_{x}\)
• De Giorgi argument for weighted \(L^2\cap L^{\infty}\) solutions to the non-cutoff Boltzmann equation
• The Vlasov-Poisson-Landau system in a periodic box
• Global classical solutions of the Boltzmann equation without angular cut-off
• Dissipation and Semigroup on $H^k_n$: Non-cutoff Linearized Boltzmann Operator with Soft Potential
• Global weak solutions of Vlasov‐Maxwell systems
• Hypocoercivity
• Boltzmann collision operator with inverse‐power intermolecular potentials, I
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• The Boltzmann equation in the whole space
• Global Mild Solutions of the Landau and <scp>Non‐Cutoff</scp> Boltzmann Equations
• Almost Exponential Decay Near Maxwellian
• THE BOLTZMANN EQUATION IN THE SPACE $L^2\cap L^\infty_\beta$: GLOBAL AND TIME-PERIODIC SOLUTIONS
• Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus
• Explicit Coercivity Estimates for the Linearized Boltzmann and Landau Operators