Robert M. Strain

Almost Exponential Decay Near Maxwellian

ABSTRACT By direct interpolation of a family of smooth energy estimates for solutions near Maxwellian equilibrium and in a periodic box to several Boltzmann type equations in Guo (2002 2003a b) and Strain and Guo (2004), we show convergence to Maxwellian with any polynomial rate in time. Our results not only resolve the important open problem for both the Vlasov-Maxwell-Boltzmann system and the relativistic Landau-Maxwell system for charged particles, but also lead to a simpler alternative proof of recent decay results (Desvillettes and Villani, 2005) for soft potentials as well as the Coulombic interaction, with precise decay rate depending on the initial conditions.

Global classical solutions of the Boltzmann equation without angular cut-off

This work proves the global stability of the Boltzmann equation (1872) with the physical collision kernels derived by Maxwell in 1866 for the full range of inverse-power intermolecular potentials,

The Vlasov–Maxwell–Boltzmann System in the Whole Space

r^{-(p-1)}

Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff

with

Optimal large‐time behavior of the Vlasov‐Maxwell‐Boltzmann system in the whole space

p>2

On the global existence for the Muskat problem

, for initial perturbations of the Maxwellian equilibrium states, as announced in \cite{gsNonCutA}. We more generally cover collision kernels with parameters

Lower Bounds on the Blow-Up Rate of the Axisymmetric Navier–Stokes Equations II

s\in (0,1)

Global classical solutions of the Boltzmann equation with long-range interactions

and

The Boltzmann equation, Besov spaces, and optimal time decay rates in Rxn

\gamma

Lower Bound on the Blow-up Rate of the Axisymmetric Navier–Stokes Equations

satisfying