On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation

By Laurent Desvillettes, Cédric Villani. 2005

441 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5984f6324fef060e006bdd5549623a5b6a142319

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

The weak Harnack inequality for the Boltzmann equation without cut-off (2016, background): “For example, Desvillettes and Villani prove in [31] that the solutions converge to equilibrium, at a specific rate, provided that the solution remains smooth.”
Non-Isothermal Boundary in the Boltzmann Theory and Fourier Law (2013, background): “2) at a given constant temperature θ (isothermal), has an equilibrium state described by the Maxwellian constant × e−|v|2/2θ, and it is well known [35, 10, 18, 12, 39, 22, 38] that such an equilibrium is reached exponentially fast, at least if the initial state is close to the above Maxwellian in a ”
Almost Exponential Decay Near Maxwellian (2006, neutral): “Mathematics Subject Classification 82B40; 82C40; 82D05; 82D10.”
Exponential decay toward equilibrium via entropy methods for reaction–diffusion equations (2006, background): “), integral equations (such as the spatially homogeneous Boltzmann equation [40–42]), or kinetic equations [6,14,15,17].”
Hypocoercivity (2006, methodology): “8 can be understood as a very abstract reformulation of the property of “instability of hydrodynamic description” introduced in [15].”
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds (2008, background): “), integral equations (such as the spatially homogeneous Boltzmann equation [33, 34, 35]), or kinetic equations ([3], [12, 13], [14]).”
Exponential Decay for Soft Potentials near Maxwellian (2008, background): “Our results extend the classical result Caflisch of [2] to the case of very soft potential and Coulomb interactions, and also improve the recent “almost exponential” decay results by [5, 14].”
Hypocoercive Diffusion Operators (2006, methodology): “As discussed in [5], all these estimates can be proven in the close-toequilibrium regime, but remain a major open problem for solutions in the large.”
Factorization for non-symmetric operators and exponential H-theorem (2010, methodology): “This is based on the idea of connecting the nonlinear theory in [12] with the linearized theory developped in [24] and it makes crucial use of our new method for enlarging the space of decay estimates on semigroups.”
Global classical solutions of the Boltzmann equation without angular cut-off (2009, background): “revised, posted, and combined into three papers. These new papers do not obtain the optimal time decay rates for the soft potentials in the whole space. 20 P. T. GRESSMAN AND R. M. STRAIN We refer to [8,20,35,36,75,76,82], and the references therein, in this regard, to mention only a brief few works”