Stability and exponential convergence for Boltzmann equation

DOI10.1007/BF00375152zbMath0828.76076MaRDI QIDQ1894120

Bernt Wennberg

Publication date: 18 July 1995

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

existenceuniquenessperiodic boxMaxwellian interactionsspatially homogeneous equation

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05)

Related Items

Uniqueness and long time asymptotic for the Keller-Segel equation: the parabolic-elliptic case ⋮ Spectral analysis of semigroups and growth-fragmentation equations ⋮ The solution of the nonlinear Boltzmann equation: A survey of analytic and computational methods ⋮ The spectrum of the transport operator with a potential term under the spatial periodicity condition ⋮ On the cutoff approximation for the Boltzmann equation with long-range interaction ⋮ Propagation of Moments and Sharp Convergence Rate for Inhomogeneous Noncutoff Boltzmann Equation with Soft Potentials ⋮ An application of the Kantorovich-Rubinstein maximum principle in the theory of the Tjon-Wu equation ⋮ Upper Maxwellian bounds for the Boltzmann equation with pseudo-Maxwell molecules ⋮ On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation ⋮ On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications ⋮ UNIFORM L^p-STABILITY ESTIMATE FOR THE SPATIALLY INHOMOGENEOUS BOLTZMANN EQUATION NEAR VACUUM ⋮ \(L ^{2}\)-stability theory of the Boltzmann equation near a global Maxwellian ⋮ The Boltzmann Equation over $${{\mathbb R}^{{\mathrm {D}}}}$$ R D : Dispersion Versus Dissipation ⋮ L p stability of solutions of Boltzmann equation with external force in soft potentials ⋮ Decay of solutions to the mixed problem for the linearized Boltzmann equation with a potential term in a polyhedral bounded domain

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• Semigroups of linear operators and applications to partial differential equations
• \(L^{\infty}\) estimates for the space-homogeneous Boltzmann equation
• The Boltzmann equation: global existence for a rare gas in an infinite vacuum
• On the Boltzmann equation in unbounded space far from equilibrium, and the limit of zero mean free path
• \(L^ p\)-estimates for the nonlinear spatially homogeneous Boltzmann equation
• Regularity of the moments of the solution of a transport equation
• Existence theorems for certain kinetic equations and large data
• Stability in \(L^ 1\) for the spatially homogeneous Boltzmann equation
• Global \(L^ p\)-properties for the spatially homogeneous Boltzmann equation
• On the nonlinear Boltzmann equation in unbounded domains
• The Boltzmann equation for weakly inhomogeneous data
• The Boltzmann equation with a soft potential. I: Linear, spatially- homogeneous
• Spectral methods in linear transport theory
• Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range
• Real and complex interpolation and extrapolation of compact operators
• One-sided compactness results for Aronszajn-Gagliardo functors
• The Boltzmann equation and its applications
• Some applications of the method of moments for the homogeneous Boltzmann and Kac equations
• Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator
• On the Boltzmann equation. II: The full initial value problem
• On theH-Function and Convergence Towards Equilibrium for a Space-Homogeneous Molecular Density
• Spectral properties of the space nonhomogeneous linearized Boltzmann operator
• Evolution operators generated by tee space and time nonhomogeneous lineartzed Boltzmann operator
• On the StrongL¹Trend to Equilibrium for the Boltzmann Equation
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• On moments and uniqueness for solutions to the space homogeneous Boltzmann equation
• Stability and exponential convergence in Lp for the spatially homogeneous Boltzmann equation
• Equivalent Norms for Sobolev Spaces
• Asymptotic Theory of the Boltzmann Equation