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ВИДЕОТЕКА |
Geometric Measure Theory and Geometric Analysis in Moscow
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On the sticky particle solutions to the multi-dimensional pressureless Euler equations S. Bianchini |
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Аннотация: In this talk we consider the multi-dimensional pressureless Euler system \begin{equation*} \left\{\begin{aligned} &\partial_t\rho+\mathrm{div}(\rho v)=0 \ &\partial_t(\rho v)+\mathrm{div}(\rho v\otimes v)=0, \end{aligned}\right. \end{equation*} where In this paper we prove that for a comeager set of initial data in the weak topology the pressureless Euler system admits a unique sticky particle solution given by a free flow where trajectories are disjoint straight lines. Indeed, such an existence and uniqueness result holds for a broader class of solutions decreasing their kinetic energy, which we call dissipative solutions, and which turns out to be the compact weak closure of the classical sticky particle solutions. Therefore any scheme for which the energy is l.s.c. and is dissipated will converge, for a comeager set of data, to our solution, i.e. the free flow. Язык доклада: английский |