scholarly journals Existence of local strong solutions to fluid–beam and fluid–rod interaction systems

2019 ◽  
Vol 36 (4) ◽  
pp. 1105-1149 ◽  
Author(s):  
Céline Grandmont ◽  
Matthieu Hillairet ◽  
Julien Lequeurre
Keyword(s):  
Strong Solutions ◽  
Local Strong Solutions

Local existence and Serrin-type blow-up criterion for strong solutions to the radiation hydrodynamic equations

2020 ◽  
Vol 17 (03) ◽  
pp. 501-557
Author(s):  
Hao Li ◽  
Yachun Li
Keyword(s):  
Blow Up ◽  
Initial Density ◽  
Local Existence ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Hydrodynamic Equations ◽  
Open Set ◽  
The Cauchy Problem ◽  
Local Strong Solutions ◽  
Blow Up Criterion

We consider the Cauchy problem for the three-dimensional, compressible radiation hydrodynamic equations. We establish the existence and uniqueness of local strong solutions for large initial data satisfying some compatibility condition. The initial density need not be positive and may vanish in an open set. Moreover, we establish a Serrin-type blow-up criterion, which is stated in terms of the velocity and density variables [Formula: see text] and is independent of the temperature and the radiation intensity.

A regularity criterion for local strong solutions to the 3D Stokes-MHD equations

2020 ◽  
Vol 124 (3) ◽  
pp. 247-255
Author(s):  
Ahmad Mohammad Alghamdi ◽  
Sadek Gala ◽  
Maria Alessandra Ragusa
Keyword(s):  
Strong Solutions ◽  
Regularity Criterion ◽  
Mhd Equations ◽  
Local Strong Solutions

scholarly journals Local Strong Solution for a Class of Shear Thickening Fluids with Non-Newtonian Potential and Heat-Conducting

2015 ◽  
Vol 2015 ◽  
pp. 1-17
Author(s):  
Yunliang Zhang ◽  
Zhidong Guo
Keyword(s):  
Existence And Uniqueness ◽  
Shear Thickening ◽  
Strong Solutions ◽  
Newtonian Potential ◽  
State Function ◽  
Heat Conducting ◽  
Strong Nonlinearity ◽  
Shear Thickening Fluids ◽  
Local Strong Solutions ◽  
Local Strong Solution

The aim of this paper is to discuss the model for a class of shear thickening fluids with non-Newtonian potential and heat-conducting. Existence and uniqueness of local strong solutions for the model are proved. In this paper, there exist two difficulties we have to overcome. One is the strong nonlinearity of the system. The other is that the state function is not fixed.

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