Global Smooth Solutions to the 2-D Inhomogeneous Navier–Stokes Equations with Variable Viscosity

2013 ◽  
pp. 63-91 ◽  
Author(s):  
Guilong Gui
Keyword(s):  
Stokes Equations ◽  
Variable Viscosity ◽  
Navier Stokes ◽  
Smooth Solutions ◽  
Navier Stokes Equations ◽  
Global Smooth Solutions

Some stability results on global solutions to the Navier–Stokes equations

Analysis ◽  
2015 ◽  
Vol 35 (3) ◽  
Author(s):  
Isabelle Gallagher
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Global Solutions ◽  
Navier Stokes ◽  
Smooth Solutions ◽  
Navier Stokes Equations ◽  
Global Smooth Solutions ◽  
Whole Space ◽  
The Stability ◽  
Stability Results

AbstractIn these notes we present some results concerning the existence of global smooth solutions to the three-dimensional Navier–Stokes equations set in the whole space. We are particularly interested in the stability of the set of initial data giving rise to a global smooth solution.

scholarly journals Vortex reconnections in classical and quantum fluids

SeMA Journal ◽  
2021 ◽  
Author(s):  
Alberto Enciso ◽  
Daniel Peralta-Salas
Keyword(s):  
Stokes Equations ◽  
Quantum Fluids ◽  
Navier Stokes ◽  
Pitaevskii Equation ◽  
Global Approximation ◽  
Rigorous Results ◽  
Navier Stokes Equations ◽  
Localization Principle ◽  
Global Smooth Solutions ◽  
Vortex Reconnection

AbstractWe review recent rigorous results on the phenomenon of vortex reconnection in classical and quantum fluids. In the context of the Navier–Stokes equations in $$\mathbb {T}^3$$ T 3 we show the existence of global smooth solutions that exhibit creation and destruction of vortex lines of arbitrarily complicated topologies. Concerning quantum fluids, we prove that for any initial and final configurations of quantum vortices, and any way of transforming one into the other, there is an initial condition whose associated solution to the Gross–Pitaevskii equation realizes this specific vortex reconnection scenario. Key to prove these results is an inverse localization principle for Beltrami fields and a global approximation theorem for the linear Schrödinger equation.

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