Global Existence and Uniqueness of Weak Solutions of Three-Dimensional Euler Equations with Helical Symmetry in the Absence of Vorticity Stretching

2009 ◽  
Vol 41 (1) ◽  
pp. 269-296 ◽  
Author(s):  
Boris Ettinger ◽  
Edriss S. Titi
Keyword(s):  
Global Existence ◽  
Euler Equations ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Three Dimensional ◽  
Helical Symmetry ◽  
Global Existence And Uniqueness

scholarly journals The Cauchy Problem for the Incompressible 2D-MHD with Power Law-Type Nonlinear Viscous Fluid

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jae-Myoung Kim
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Global Existence ◽  
Viscous Fluid ◽  
Power Law ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Fluid Flows ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We investigate a motion of the incompressible 2D-MHD with power law-type nonlinear viscous fluid. In this paper, we establish the global existence and uniqueness of a weak solution u , b depending on a number q in ℝ 2 . Moreover, the energy norm of the weak solutions to the fluid flows has decay rate 1 + t − 1 / 2 .

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