Euler–Poisson systems as action-minimizing paths in the Wasserstein space

Adrian Tudorascu
Georgia Institute of Technology

In this talk I will describe a variational approach employed to establish existence of solutions for the one-dimensional pressureless repulsive Euler-Poisson system with uniform background charge. We assume that the initial and terminal points are prescribed in the set of Borel probabilities with finite second-order moments. Uniqueness of these minimizing paths is also obtained for finite time. By analyzing the Lagrangian formulation of the problem,
these solutions are shown to conserve the energy of the system. Joint work with: W. Gangbo & T. Nguyen

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