Abstract integrodifferential equations and applications
Analysis of PDEs
2026-02-10 v1
Abstract
In this work, we study the initial value problem associated with an abstract integrodifferential equation in interpolation scales. We prove local-in-time existence, uniqueness, continuation, and a blow-up alternative for regular mild solutions to the problem. Additionally, we apply this theory to the Navier-Stokes equations with hereditary viscosity, taking initial data in the scale of fractional power spaces associated with the Stokes operator. We also explore reaction-diffusion problems with memory, considering the effects of super-linear and gradient-type nonlinearities, and initial data in Lebesgue and Besov spaces, respectively.
Cite
@article{arxiv.2602.08691,
title = {Abstract integrodifferential equations and applications},
author = {Bruno de Andrade and Marcos Gabriel de Santana},
journal= {arXiv preprint arXiv:2602.08691},
year = {2026}
}
Comments
46 pages