SOLUTIONS OF AN ADVECTED PHASE FIELD SYSTEM WITH LOW REGULARITY VELOCITY

Author(s)

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

Affiliation

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

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

• Document type: Journal article
• Source: Proceedings of the American Mathematical Society; v. 141, n. 3, p. 943-958, MAR 2013.
• Web of Science Citations: 0

Abstract

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)

• FAPESP's process: 10/10087-8 - Control and decay for partial differential equation systems
• Grantee: Bianca Morelli Rodolfo Calsavara
• Support Opportunities: Regular Research Grants