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Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains Ω t + , Ω t − ⊂ R N , N ≥ 2 , where the domains are separated by a sharp compact interface Γ t ⊂ R N − 1 . We prove a global in time unique existence theorem for such free boundary problem under the assumption that the initial data are sufficiently small and the initial domain of the incompressible fluid is close to a ball. In particular, we obtain the solution in the maximal L p − L q -regularity class with 2 < p < ∞ and N < q < ∞ and exponential stability of the corresponding analytic semigroup on the infinite time interval. [ABSTRACT FROM AUTHOR]

We present some fundamental results concerning to continuous quasi gyrolinear operators between Möbius gyrovector spaces induced by finite matrices. Such mappings are significant like as operators induced by matrices between finite dimensional Hilbert spaces. This gives a novel approach to the study of mappings between Möbius gyrovector spaces that should correspond to bounded linear operators on real Hilbert spaces. [ABSTRACT FROM AUTHOR]