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

@inproceedings{Gangbo2008EulerP,
  title={Euler – Poisson systems as action-minimizing paths in the Wasserstein space},
  author={Wilfrid Gangbo and Truyen Nguyen and Adrian Tudorascu},
  year={2008}
}
This paper uses a variational approach to establish existence of solutions (σt, vt) for the 1–d Euler-Poisson system by minimizing an action. We assume that the initial and terminal points σ0, σT are prescribed in P2(IR), the set of Borel probability measures on the real line, of finite second-order moments. We show existence of a unique minimizer of the action when the time interval [0, T ] satisfies T < π. These solutions conserve the Hamiltonian and they yield a path t → σt in P2(IR). When… CONTINUE READING
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