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.