对二维无旋可压缩Euler方程,当其初值是一个常态的小扰动时,我们证明 了ρ,ν的一阶导数在爆破时刻同时破裂,从而对无旋情形证明了Alinhac S.的猜测.

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 ρ, v blow up at the blowup time while ρ, v remain continuous. In particular, in the irrotational case we prove Alinhac's S. conjecture.