Ice formation in the Arctic during summer: false-bottoms

Phan Thanh Nam (1) , Alain Pham Ngoc Dinh (2) , Pham Hoang Quan (3, 4) , Dang Duc Trong (3)

1 UNS-HCMC - Mathematics Department
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 UNS-HCMC - University of Natural Sciences- HoChiMinh City
4 Mathematics department

The only source of ice formation in the Arctic during summer is a layer of ice called false-bottoms between an under-ice melt pond and the underlying ocean. Of interest is to give a mathematical model in order to determine the simultaneous growth and ablation of false-bottoms, which is governed by both of heat fluxes and salt fluxes. In one dimension, this problem may be considered mathematically as a two-phase Stefan problem with two free boundaries. Our main result is to prove the existence and uniqueness of the solution from the initial condition.

Mots clés: False-bottoms; Free boundary problem; Green's function; Contraction Mapping Principle

Domaines: Equations aux dérivées partielles [math.AP]

Phan Thanh Nam, Alain Pham Ngoc Dinh, Pham Hoang Quan, Dang Duc Trong. Ice formation in the Arctic during summer: false-bottoms. Applied Mathematics and Computation, 2014, 227, pp.857-870. ⟨10.1016/j.amc.2013.11.003⟩. ⟨hal-00297325v2⟩