WELL-POSEDNESS AND SINGULARITY FORMATION FOR VLASOV-RIESZ SYSTEM

We investigate the Cauchy problem for the Vlasov-Riesz system, which is a Vlasov equation featuring an interaction potential generalizing previously studied cases, including the Coulomb & phi; = (- increment )-1 & rho;, Manev (- increment )-1+ (- increment )-2, and pure Manev (- increment )- 1 1 2 potentials. For the first time, we extend the local theory of classical solutions to potentials more singular than that for the Manev. Then, we obtain finite-time singularity formation for solutions with various attractive interaction potentials, extending the well-known blowup result for attractive Vlasov-Poisson for d & GE; 4. Our local well-posedness and singularity formation results extend to cases when linear diffusion and damping in velocity are present.