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Document Type:	Dissertação
Title:	Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications
Authors:	Santana, Marcos Gabriel de
Issue Date:	26-Feb-2021
Advisor:	Santos, Bruno Luis de Andrade
Resumo :	In this work, we study the initial value problem associated with the abstract integrodifferential equation u'(t) = S g(t − s)Au(s)ds + f(t, u(t)), t > 0, with critical or subcritical nonlinearity f in interpolation scales. We prove local-in-time existence, uniqueness, continuation, and blow-up alternative of the E-regular solution that satisfies a specific 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 nonlinearities, and initial data in Lebesgue and Besov spaces, respectively.
Keywords:	Matemática Equações diferenciais não-lineares Equações de Navier-Stokes Integrodifferential equations Critical nonlinearities Local well-posedness Continuation and blow-up alternative Regularity theory Navier-Stokes with hereditary viscosity Reaction-diffusion with memory
Subject CNPQ:	CIENCIAS EXATAS E DA TERRA::MATEMATICA
Sponsorship:	Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Language:	eng
Institution:	Universidade Federal de Sergipe
Program Affiliation:	Pós-Graduação em Matemática
Citation:	SANTANA, Marcos Gabriel de. Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications. 2021. 107 f. Dissertação (Mestrado em Matemática) – Universidade Federal de Sergipe, São Cristóvão, 2021.
URI:	http://ri.ufs.br/jspui/handle/riufs/16245
Appears in Collections:	Mestrado em Matemática

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