The Navier-Stokes equation with distributions as initial data and application to self-similar solutions

1997 ◽  
pp. 125-141 ◽  
Author(s):  
Hideo Kozono ◽  
Masao Yamazaki
Keyword(s):  
Initial Data ◽  
Stokes Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Self Similar ◽  
Similar Solutions

Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids

2019 ◽  
Vol 26 (1/2) ◽  
pp. 167-178 ◽  
Author(s):  
Dongming Wei ◽  
Samer Al-Ashhab
Keyword(s):  
Newtonian Fluids ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Infinite Domain ◽  
Navier Stokes Equation ◽  
Continuity Equations ◽  
Self Similar ◽  
Similar Solutions ◽  
Two Parameters

The reduced problem of the Navier–Stokes and the continuity equations, in two-dimensional Cartesian coordinates with Eulerian description, for incompressible non-Newtonian fluids, is considered. The Ladyzhenskaya model, with a non-linear velocity dependent stress tensor is adopted, and leads to the governing equation of interest. The reduction is based on a self-similar transformation as demonstrated in existing literature, for two spatial variables and one time variable, resulting in an ODE defined on a semi-infinite domain. In our search for classical solutions, existence and uniqueness will be determined depending on the signs of two parameters with physical interpretation in the equation. Illustrations are included to highlight some of the main results.

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