scholarly journals Global solvability of the free-boundary problem for one-dimensional motion of a self-gravitating viscous radiative and reactive gas

2008 ◽  
Vol 84 (7) ◽  
pp. 123-128 ◽  
Author(s):  
Morimichi Umehara ◽  
Atusi Tani
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Global Solvability ◽  
One Dimensional ◽  
Reactive Gas

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.

scholarly journals On the Solution of a Hyperbolic One-Dimensional Free Boundary Problem for a Maxwell Fluid

2011 ◽  
Vol 2011 ◽  
pp. 1-26
Author(s):  
Lorenzo Fusi ◽  
Angiolo Farina
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Boundary Data ◽  
Inner Core ◽  
Representation Formula ◽  
Maxwell Fluid ◽  
Explicit Representation ◽  
Boundary Equation ◽  
One Dimensional

We study a hyperbolic (telegrapher's equation) free boundary problem describing the pressure-driven channel flow of a Bingham-type fluid whose constitutive model was derived in the work of Fusi and Farina (2011). The free boundary is the surface that separates the inner core (where the velocity is uniform) from the external layer where the fluid behaves as an upper convected Maxwell fluid. We present a procedure to obtain an explicit representation formula for the solution. We then exploit such a representation to write the free boundary equation in terms of the initial and boundary data only. We also perform an asymptotic expansion in terms of a parameter tied to the rheological properties of the Maxwell fluid. Explicit formulas of the solutions for the various order of approximation are provided.

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