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Instantaneous blow-up of solutions to the Cauchy problem for the fractional Khokhlov-Zabolotskaya equation
Journal article   Open access  Peer reviewed

Instantaneous blow-up of solutions to the Cauchy problem for the fractional Khokhlov-Zabolotskaya equation

Mohamed Jleli
Open mathematics (Warsaw, Poland), Vol.18(1), pp.1266-1271
20/11/2020
DOI: https://doi.org/10.1515/math-2020-0089

Abstract

26A33 blow-up fractional differential equations nonlinear capacity
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.
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https://doi.org/10.1515/math-2020-0089View
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