Yin, Huicheng; Zheng, Qin; Jin, Shu Ze The blow up of solutions for two-dimensional irrotational compressible Euler equations. (Chinese. English summary) Zbl 1028.35093 Acta Math. Sin. 46, No. 2, 351-360 (2003). 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)]. MSC: 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 Keywords:commutator method; Nash-Moser iteration PDF BibTeX XML Cite \textit{H. Yin} et al., Acta Math. Sin. 46, No. 2, 351--360 (2003; Zbl 1028.35093)