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The blow up of solutions for two-dimensional irrotational compressible Euler equations. (Chinese. English summary) Zbl 1028.35093
Summary: For two-dimensional irrotational compressible Euler equations with initial data that is a small perturbation from a constant state, we prove that the first-order derivatives of \(\rho\), \(v\) blow up at the blow up time while \(\rho\), \(v\) remain continuous. In particular, in the irrotational case we prove S. Alinhac’s conjecture [Acta Math. 182, 1-23 (1999; Zbl 0973.35135)].
35L45 Initial value problems for first-order hyperbolic systems
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs