Geodesic
Instantaneous blow-up of classical solutions to the Cauchy problem for the Khokhlov–Zabolotskaya equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1170-1175

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The Cauchy problem for a second-order nonlinear equation with mixed derivatives is considered. It is proved that its classical local-in-time solution does not exist. The blow-up of the solution is proved by applying S. I. Pohozaev and E. L. Mitidieri's nonlinear capacity method. 
@article{ZVMMF_2017_57_7_a7,
     author = {M. O. Korpusov and S. G. Mikhailenko},
     title = {Instantaneous blow-up of classical solutions to the {Cauchy} problem for the {Khokhlov{\textendash}Zabolotskaya} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1170--1175},
     publisher = {mathdoc},
     volume = {57},
     number = {7},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a7/}
}
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M. O. Korpusov; S. G. Mikhailenko. Instantaneous blow-up of classical solutions to the Cauchy problem for the Khokhlov–Zabolotskaya equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1170-1175. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a7/