SOLUTIONS OF AN ADVECTED PHASE FIELD SYSTEM WITH LOW REGULARITY VELOCITY

Autor(es)

Rodolfo Calsavara, Bianca Morelli ^[1] ; Boldrini, Jose Luiz ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, UNICAMP, Sch Appl Sci, BR-13484350 Limeira, SP - Brazil

^[2] Univ Estadual Campinas, UNICAMP, IMECC, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 141, n. 3, p. 943-958, MAR 2013.
• Citações Web of Science: 0

Resumo

We present a result on existence of solutions for a system of highly nonlinear partial differential equations related to a phase field model for non-isothermal solidification/melting processes in the case of two possible crystallization states and flow of the molten material. The flow is incompressible with a velocity which is assumed to be given, but with low regularity. We prove the existence of solutions for the associated system and also give estimates for the temperature and the phase fields related to each of the crystallization states in terms of the low regularity norms of the given flow velocity. These results constitute a fundamental step in the proof of the existence of solutions of a complete model for solidification obtained by coupling the present equations with a singular Navier-Stokes system for the flow velocity. The analysis of this complete model is done in a forthcoming article. (AU)

• Processo FAPESP: 10/10087-8 - Controle e decaimento para sistemas de equações diferenciais parciais
• Beneficiário: Bianca Morelli Rodolfo Calsavara
• Modalidade de apoio: Auxílio à Pesquisa - Regular