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A variational time discretization for compressible Euler equations. (English) Zbl 1501.35287

Summary: We introduce a variational time discretization for the multidimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each time step requires the minimization of a functional measuring the acceleration of fluid elements, over the cone of monotone transport maps. We prove convergence to measure-valued solutions for the pressureless gas dynamics and the compressible Euler equations. For one space dimension, we obtain sticky particle solutions for the pressureless case.

MSC:

35Q31 Euler equations
76N15 Gas dynamics (general theory)
35L65 Hyperbolic conservation laws
49J40 Variational inequalities
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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