# zbMATH — the first resource for mathematics

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)].
##### 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