Abstract In this paper, we consider the Cauchy problem for a second-order nonlinear equation with mixed fractional derivatives related to the fractional Khokhlov-Zabolotskaya equation. We prove the nonexistence of a classical local in time solution. The obtained instantaneous blow-up result is proved via the nonlinear capacity method.

中文翻译：

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分数阶 Khokhlov-Zabolotskaya 方程柯西问题解的瞬时爆炸

摘要 在本文中，我们考虑了与分数阶 Khokhlov-Zabolotskaya 方程相关的具有混合分数阶导数的二阶非线性方程的柯西问题。我们证明了经典的局部时间解不存在。通过非线性容量方法证明了获得的瞬时爆破结果。