Global classical solutions to the one dimensional free boundary problem for compressible non-isothermal liquid crystal flow with large data

2020 ◽  
Vol 269 (10) ◽  
pp. 8055-8106
Author(s):  
Yu Mei
Keyword(s):  
Liquid Crystal ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Large Data ◽  
Classical Solutions ◽  
One Dimensional ◽  
Global Classical Solutions ◽  
Liquid Crystal Flow ◽  
The One

Long-time existence of classical solutions to a one-dimensional swelling gel

2014 ◽  
Vol 25 (01) ◽  
pp. 165-194 ◽  
Author(s):  
M. Carme Calderer ◽  
Robin Ming Chen
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Lagrangian Formulation ◽  
Classical Solutions ◽  
Governing Equations ◽  
Fixed Boundary ◽  
One Dimensional ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

In this paper, we derived a model which describes the swelling dynamics of a gel and study the system in one-dimensional geometry with a free boundary. The governing equations are hyperbolic with a weakly dissipative source. Using a mass-Lagrangian formulation, the free boundary is transformed into a fixed boundary. We prove the existence of long-time C1-solutions to the transformed fixed boundary problem.

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