BOLTZMANN EQUATION WITH INFINITE ENERGY - RENORMALIZED SOLUTIONS AND DISTRIBUTIONAL SOLUTIONS FOR SMALL INITIAL DATA AND INITIAL DATA CLOSE TO A MAXWELLIAN

摘要

We prove new existence results for the Boltzmann equation with an initial data with infinite energy, In the framework of renormalized solutions we assume (x(alpha) + x - v(2)) f(0) is an element of L-1 instead of (x(2) + (2)) f(0) is an element of L-1, and we show new a priori estimates. In the framework of distributional solutions we treat small initial data compared to a Maxwellian of the type exp(-x -v(2)/2). We also treat initial data close enough to such a Maxwellian. Hence, our theory does not require that the initial data decrease in both variables x and v. [References: 20]