Instantaneous blow-up of solutions to the Cauchy problem for the fractional Khokhlov-Zabolotskaya equation. (English) Zbl 1484.35085
Summary: 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.
MSC:
| 35B44 | Blow-up in context of PDEs |
| 35Q35 | PDEs in connection with fluid mechanics |
| 35R11 | Fractional partial differential equations |
| 26A33 | Fractional derivatives and integrals |
Keywords:
nonlinear capacity method; Cauchy problem; nonexistence of a local in time classical solutionReferences:
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