Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
DISCENTE: MARCOS GABRIEL DE SANTANA
DATA: 26/02/2021
HORA: 10:00
LOCAL: Universidade Federal de Sergipe
TÍTULO: WELL POSEDNESS AND REGULARITY THEORY TO ABSTRACT INTEGRO-DIFFERENTIAL EQUATIONS IN INTERPOLATION SCALES AND APPLICATIONS
PALAVRAS-CHAVES: Integro-differential equations, Critical non-linearities, Local well-posedness, Regularity theory, Navier-Stokes with hereditary viscosity, Reaction-diffusion with memory.
PÁGINAS: 107
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Matemática
SUBÁREA: Análise
ESPECIALIDADE: Equações Diferenciais Parciais
RESUMO:
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.