Banca de DEFESA: MARCOS GABRIEL DE SANTANA
20/02/2021 10:58
In this work, we study the initial value problem associated with a class of abstract integro-differential equations with critical or sub-critical non-linearity in interpolation scales. We prove the local-in-time existence, uniqueness, continuation, and blow-up alternative of the ε-regular solution that satisfies a certain condition of controlled behavior at t = 0. Then, we apply the theory to the Navier-Stokes problem with hereditary viscosity and initial data in the scale of fractional power spaces associated with the Stokes operator; and to reaction-diffusion problems with super-linear and gradient non-linearities, and initial data in Lebesgue and Besov spaces, respectively.
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