Global Well-Posedness of the Generalized Incompressible Navier–Stokes Equations with Large Initial Data

2019 ◽  
Vol 43 (3) ◽  
pp. 2549-2564 ◽  
Author(s):  
Qiao Liu
Keyword(s):  
Initial Data ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Well Posedness ◽  
Large Initial Data ◽  
Navier Stokes Equations

Global well-posedness for 3D Navier–Stokes equations with ill-prepared initial data

2013 ◽  
Vol 13 (2) ◽  
pp. 395-411 ◽  
Author(s):  
Marius Paicu ◽  
Zhifei Zhang
Keyword(s):  
Initial Data ◽  
Blow Up ◽  
Stokes Equations ◽  
Vertical Direction ◽  
Navier Stokes ◽  
Well Posedness ◽  
Large Initial Data ◽  
Navier Stokes Equations

AbstractWe study the global well-posedness of 3D Navier–Stokes equations for a class of large initial data. This type of data slowly varies in the vertical direction (expressed as a function of $\varepsilon {x}_{3} $), and it is ill-prepared in the sense that its norm in ${C}^{- 1} $ will blow up at the rate ${\varepsilon }^{- \alpha } $ for $\frac{1}{2} \lt \alpha \lt 1$ as $\varepsilon $ tends to zero.

scholarly journals GLOBAL SOLUTION FOR THE GENERALIZED ANISOTROPIC NAVIER–STOKES EQUATIONS WITH LARGE DATA

2015 ◽  
Vol 20 (2) ◽  
pp. 205-231 ◽  
Author(s):  
Daoyuan Fang ◽  
Bin Han
Keyword(s):  
Initial Data ◽  
Besov Space ◽  
Global Solution ◽  
Stokes Equations ◽  
Large Data ◽  
Navier Stokes ◽  
Unique Global Solution ◽  
Large Initial Data ◽  
Navier Stokes Equations ◽  
Anisotropic Besov Space

We are concerned with 3D incompressible generalized anisotropic Navier– Stokes equations with hyperdissipative term in horizontal variables. We prove that there exists a unique global solution for it with large initial data in anisotropic Besov space.

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