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math.AP2024
Variational interacting particle systems and Vlasov equations
Peter Gladbach, Bernhard Kepka
We consider optimization problems for interacting particle systems. We show that critical points solve a Vlasov equation, and that in general no minimizers exist despite continuity…
math.AP2023
Rotating solutions to the incompressible Euler-Poisson equation with external particle
Diego Alonso-Orán, Bernhard Kepka, Juan J. L. Velázquez
We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configur…