A combination of energy method and spectral analysis for study of equations of gas motion

DOI10.1007/s11464-009-0020-xzbMath1180.35103OpenAlexW2043520400MaRDI QIDQ1042542

Seiji Ukai, Renjun Duan, Tong Yang

Publication date: 14 December 2009

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-009-0020-x

zbMATH Keywords

linearizationasymptotic stabilityVlasov-Poisson-Boltzmann systemoptimal ratenon-trivial steady statetime-space dependent forces

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Navier-Stokes equations (35Q30) Boltzmann equations (35Q20)

Related Items

GREEN'S FUNCTION AND LARGE TIME BEHAVIOR OF THE NAVIER–STOKES–MAXWELL SYSTEM, Global existence and exponential stability for the strong solutions in \(H^{2}\) to the 3-D chemotaxis model, Darcy's law and diffusion for a two-fluid Euler–Maxwell system with dissipation, Optimal time decay of the Boltzmann equation with frictional force, Global existence and decay estimates of the Boltzmann equation with frictional force: the general results, Time periodic solutions of compressible Navier-Stokes equations, Global existence and full regularity of the Boltzmann equation without angular cutoff, A kinetic flocking model with diffusion, Energy method for multi-dimensional balance laws with non-local dissipation, GLOBAL SMOOTH FLOWS FOR THE COMPRESSIBLE EULER–MAXWELL SYSTEM: THE RELAXATION CASE, Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space, Ellipsoidal BGK model near a global Maxwellian in the whole space, THE VLASOV–POISSON–BOLTZMANN SYSTEM FOR SOFT POTENTIALS

Cites Work

• Unnamed Item
• Unnamed Item
• Energy method for Boltzmann equation
• Some estimates of solutions for the equations of motion of compressible viscous fluid in the three-dimensional exterior domain
• On the Cauchy problem for the Boltzmann equation in the whole space: Global existence and uniform stability in \(L_{\xi}^{2}(H_{x}^{N})\)
• The Vlasov-Maxwell-Boltzmann system in the whole space
• The initial value problem for the equations of motion of viscous and heat-conductive gases
• Decay estimates for the compressible Navier-Stokes equations in unbounded domains
• Global solutions to the initial value problem for the nonlinear Boltzmann equation
• The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd multi-dimensions
• Decay estimates of solutions for the equations of motion of compressible viscous and heat-conductive gases in an exterior domain in \(\mathbb{R}^3\)
• Pointwise decay estimates for multidimensional Navier-Stokes diffusion waves
• Boltzmann equation: micro-macro decompositions and positivity of shock profiles
• On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation
• Optimal \(L^{p}\) - \(L^{q}\) convergence rates for the compressible Navier-Stokes equations with potential force
• Convergence rate to stationary solutions for Boltzmann equation with external force
• Rate of convergence of non-stationary flow to the steady flow of compressible viscous fluid
• Optimal decay estimates on the linearized Boltzmann equation with time dependent force and their applications
• GLOBAL SOLUTIONS TO THE BOLTZMANN EQUATION WITH EXTERNAL FORCES
• Navier–Stokes equations with degenerate viscosity, vacuum and gravitational force
• A new energy method for the Boltzmann equation
• Global existence of small solutions to a class of nonlinear evolution equations
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• L²Decay for the Compressible Navier-Stokes Equations in Unbounded Domains
• The Boltzmann equation in the whole space
• Almost Exponential Decay Near Maxwellian
• Boltzmann diffusive limit beyond the Navier‐Stokes approximation
• THE BOLTZMANN EQUATION IN THE SPACE $L^2\cap L^\infty_\beta$: GLOBAL AND TIME-PERIODIC SOLUTIONS
• CONVERGENCE RATE FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH EXTERNAL FORCE
• Global weak solutions of the Navier-Stokes equations for multidimensional compressible flow subject to large external potential forces