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The blow-up of solutions for two-dimensional irrotational compressible Euler equations. (English) Zbl 0999.35075
The paper deals with the classical solution of two-dimensional Euler equations in the case of irrotational compressible fluid occupying the whole plane. The initial data contain a small perturbation from a constant state. It is proved that the first-order derivatives of the density and velocity blow-up at the blow-up time, while the density and velocity remain continuous.
MSC:
35Q35 PDEs in connection with fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q05 Euler-Poisson-Darboux equations
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