Time-Periodic Solution to the Compressible Navier-Stokes/Allen-Cahn System

2020 ◽  
Vol 36 (4) ◽  
pp. 419-442
Author(s):  
Chang Ming Song ◽  
Jian Lin Zhang ◽  
Yuan Yuan Wang
Keyword(s):  
Periodic Solution ◽  
Navier Stokes ◽  
Time Periodic ◽  
Time Periodic Solution

Periodic pattern formation in the coupled chemotaxis-(Navier–)Stokes system with mixed nonhomogeneous boundary conditions

2019 ◽  
Vol 150 (6) ◽  
pp. 3121-3152
Author(s):  
Chunhua Jin
Keyword(s):  
Periodic Solution ◽  
Pattern Formation ◽  
Fluid Model ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Periodic Pattern ◽  
Nonhomogeneous Boundary ◽  
Time Periodic Solutions ◽  
Time Periodic ◽  
Time Periodic Solution

AbstractWe consider the coupled chemotaxis-fluid model for periodic pattern formation on two- and three-dimensional domains with mixed nonhomogeneous boundary value conditions, and prove the existence of nontrivial time periodic solutions. It is worth noticing that this system admits more than one periodic solution. In fact, it is not difficult to verify that (0, c, 0, 0) is a time periodic solution. Our purpose is to obtain a time periodic solution with nonconstant bacterial density.

A note on the existence of time periodic solution of a superlinear heat equation

2018 ◽  
Vol 98 (13) ◽  
pp. 2454-2463 ◽  
Author(s):  
Haochuan Huang ◽  
Jingxue Yin ◽  
Chunhua Jin
Keyword(s):  
Periodic Solution ◽  
Heat Equation ◽  
Time Periodic ◽  
Time Periodic Solution
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