On the critical exponent "instantaneous blow-up" versus "local solubility" in the Cauchy problem for a model equation of Sobolev type

We consider the Cauchy problem for a model partial differential equation of order three with a non-linearity of the form |∇μ|q. We prove that when the Cauchy problem in ℝ3 has no local-in-time weak solution for a large class of initial functions, while when there is a local weak solution. © 2021 RAS(DoM) and LMS.

Authors
Korpusov M.O. 1 , Panin A.A. 1 , Shishkov A.E. 2
Journal
Izvestiya Mathematics
Publisher
Institute of Physics Publishing
Issue number
1
Language
English
Pages
111-144
State
Published
Link
External link
DOI
10.1070/IM8949
Volume
85
Year
2021
Organizations
  • 1 Faculty of Physics, Moscow State University, Russian Federation
  • 2 Peoples' Friendship University of Russia, Moscow, Russian Federation
Keywords
finite-time blow-up; instantaneous blow-up; non-linear waves
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