TY - JOUR

T1 - On the Global Existence of Mild Solutions to the Boltzmann Equation for Small Data in LD

AU - Arsénio, Diogo

PY - 2011/3/1

Y1 - 2011/3/1

N2 - We develop a new theory of existence of global solutions to the Boltzmann equation for small initial data. These new mild solutions are analogous to the mild solutions for the Navier-Stokes equations. The existence comes as a result of the study of the competing phenomena of dispersion, due to the transport operator, and of singularity formation, due to the nonlinear Boltzmann collision operator. It is the joint use of the so-called dispersive estimates with new convolution inequalities on the gain term of the collision operator that allows to obtain uniform bounds on the solutions and thus demonstrate the existence of solutions.

AB - We develop a new theory of existence of global solutions to the Boltzmann equation for small initial data. These new mild solutions are analogous to the mild solutions for the Navier-Stokes equations. The existence comes as a result of the study of the competing phenomena of dispersion, due to the transport operator, and of singularity formation, due to the nonlinear Boltzmann collision operator. It is the joint use of the so-called dispersive estimates with new convolution inequalities on the gain term of the collision operator that allows to obtain uniform bounds on the solutions and thus demonstrate the existence of solutions.

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U2 - 10.1007/s00220-010-1159-8

DO - 10.1007/s00220-010-1159-8

M3 - Article

AN - SCOPUS:79651475794

VL - 302

SP - 453

EP - 476

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -