Abstract integrodifferential equations and applications

Bruno de Andrade; Marcos Gabriel de Santana

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arXiv · 2602.08691

Abstract integrodifferential equations and applications

Bruno de Andrade·Marcos Gabriel de Santana

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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.

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Bruno de Andrade, Marcos Gabriel de Santana. 2026-02-09. Abstract integrodifferential equations and applications. https://arxiv.org/abs/2602.08691

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