Global classical solutions in a Keller-Segel(-Navier)-Stokes system modeling coral fertilization

2019 ◽  
Vol 267 (11) ◽  
pp. 6290-6315 ◽  
Author(s):  
Xie Li
Keyword(s):  
Stokes System ◽  
System Modeling ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Global Classical Solutions

Singular limit of a dispersive Navier–Stokes system with an entropy structure

2014 ◽  
Vol 13 (01) ◽  
pp. 77-99
Author(s):  
C. David Levermore ◽  
Weiran Sun ◽  
Konstantina Trivisa
Keyword(s):  
Stokes System ◽  
Singular Limit ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Third Order ◽  
Fluid System ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Whole Space ◽  
Entropy Structure

We prove a low Mach number limit for a dispersive fluid system [3] which contains third-order corrections to the compressible Navier–Stokes. We show that the classical solutions to this system in the whole space ℝn converge to classical solutions to ghost-effect systems [7]. Our analysis follows the framework in [4], which is built on the methodology developed by Métivier and Schochet [6] and Alazard [1] for systems up to the second order. The key new ingredient is the application of the entropy structure of the dispersive fluid system. This structure enables us to treat cases not covered in [4] and to simplify the analysis in [4].

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