Existence and Regularity of Solutions to Model for Liquid Mixture of 3He-4He

Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper. First, it is proved that this system possesses a unique global weak solution in H1(ω,C×R) by using Galerkin method. Secondly, by using an iteration procedure, regularity estimates for the linear semigroups, it is proved that the model for liquid mixture of 3He-4He has a unique solution in Hk(ω,C×R) for all k ≥ 1.