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- W2040488976 abstract "This paper uses a variational approach to establish existence of solutions (σ t , v t ) for the 1-d Euler–Poisson system by minimizing an action. We assume that the initial and terminal points σ0, σ T are prescribed in $${mathcal {P}_2(mathbb {R})}$$ , 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 → σ t in $${mathcal {P}_2(mathbb {R})}$$ . When σ t = δy(t) is a Dirac mass, the Euler–Poisson system reduces to $${ddot {y} + y=0}$$ . The kinetic version of the Euler–Poisson, that is the Vlasov–Poisson system was studied in Ambrosio and Gangbo (Comm Pure Appl Math, to appear) as a Hamiltonian system." @default.
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- W2040488976 date "2008-07-17" @default.
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- W2040488976 title "Euler–Poisson Systems as Action-Minimizing Paths in the Wasserstein Space" @default.
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- W2040488976 doi "https://doi.org/10.1007/s00205-008-0148-y" @default.
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