scholarly journals A two-phase free boundary problem with discontinuous velocity: Application to tumor model

2013 ◽  
Vol 399 (1) ◽  
pp. 378-393 ◽  
Author(s):  
Duan Chen ◽  
Avner Friedman
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Tumor Model ◽  
Two Phase

Some Free Boundary Problem for Two-Phase Inhomogeneous Incompressible Flows

2020 ◽  
Vol 52 (4) ◽  
pp. 3397-3443
Author(s):  
Hirokazu Saito ◽  
Yoshihiro Shibata ◽  
Xin Zhang
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Incompressible Flows ◽  
Two Phase

scholarly journals Global Solvability of Compressible–Incompressible Two-Phase Flows with Phase Transitions in Bounded Domains

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 258
Author(s):  
Keiichi Watanabe
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Global Solvability ◽  
Time Interval ◽  
Bounded Domains ◽  
Two Phase Flows ◽  
Two Phase ◽  
Unique Existence ◽  
A Free Boundary Problem

Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains Ωt+,Ωt−⊂RN, N≥2, where the domains are separated by a sharp compact interface Γt⊂RN−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 Lp−Lq-regularity class with 2<p<∞ and N<q<∞ and exponential stability of the corresponding analytic semigroup on the infinite time interval.

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