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Localization of the formation of singularities in multidimensional compressible Euler equationsстатья
- Автор: Rozanova Olga
- Журнал: ArXiv e-prints
- Год издания: 2020
- Номер статьи: arXiv:2010.14905
- Аннотация: We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial stationary state. We prove the blowup results using the characteristics of the propagation of the solution in space and find upper and lower bounds for the density of a smooth solution in a given region of space in terms of the initial data. To solve the problems, we introduce a special family of integral functionals and study their temporal dynamics.
- Добавил в систему: Розанова Ольга Сергеевна