2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79495We consider an equation similar to the Navier-Stokes equation. We show that there is initial data that exists in every Triebel-Lizorkin or Besov space (and hence in every Lebesgue and Sobolev space), such that after a finite time, the solution is in no Triebel-Lizorkin or Besov space (and hence in no Lebesgue or Sobolev space). The purpose is to show the limitations of the so called semigroup method for the Navier-Stokes equation. We also consider the possibility of existence of solutions with initial data in the Besov space $\dot B^{-1,\infty}_\infty$. We give initial data in this space for which there is no reasonable solution for the Navier-Stokes like equation.Also available at http://www.math.missouri.edu/~stephen/preprints/Analysis of PDEsMathematical PhysicsClassical Analysis and ODEsFunctional Analysis35Q30 46E35 (Primary); 34G20, 37L05, 47D06, 47H10 (Secondary)text