On a non-isothermal incompressible Navier-Stokes-Allen-Cahn system

Autor(es)

Honda Lopes, Juliana ^[1] ; Planas, Gabriela ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: MONATSHEFTE FUR MATHEMATIK; v. 195, n. 4, p. 687-715, AUG 2021.
• Citações Web of Science: 0

Resumo

This paper is devoted to the study of a non-isothermal incompressible Navier-Stokes-Allen-Cahn system which can be considered as a model describing the motion of the mixture of two viscous incompressible fluids. This kind of models is physically relevant for the analysis of non-isothermal fluids. The governing system of nonlinear partial differential equations consists of the Navier-Stokes equations coupled with a phase-field equation, which is the convective Allen-Cahn equation type, and an energy transport equation for the temperature. We investigate the well-posedness of the nonlinear system. More precisely, existence and uniqueness of local strong solutions in two and three dimensions for any initial data are proved. Moreover, existence of global weak solutions and existence and uniqueness of global strong solution in dimension two, when the initial temperature is suitably small, are established. (AU)

• Processo FAPESP: 19/02512-5 - Sistemas e equações diferenciais parciais
• Beneficiário: Marcelo da Silva Montenegro
• Modalidade de apoio: Auxílio à Pesquisa - Temático