scholarly journals Time-Periodic Forcing and Asymptotic Stability for the Navier-Stokes-Maxwell Equations

2017 ◽  
Vol 71 (1) ◽  
pp. 51-89
Author(s):  
S. Ibrahim ◽  
P. G. Lemarié Rieusset ◽  
N. Masmoudi
Keyword(s):  
Asymptotic Stability ◽  
Maxwell Equations ◽  
Navier Stokes ◽  
Periodic Forcing ◽  
Time Periodic

scholarly journals Weak Solutions and Their Kinetic Energy Regarding Time-Periodic Navier–Stokes Equations in Three Dimensional Whole-Space

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1528
Author(s):  
Mads Kyed
Keyword(s):  
Kinetic Energy ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Periodic Forcing ◽  
Navier Stokes Equations ◽  
Whole Space ◽  
Time Periodic Solutions ◽  
Time Periodic

The existence of weak time-periodic solutions to Navier–Stokes equations in three dimensional whole-space with time-periodic forcing terms are established. The solutions are constructed in such a way that the structural properties of their kinetic energy are obtained. No restrictions on either the size or structure of the external force are required.

scholarly journals Periodic Solution and Asymptotic Stability for the Magnetohydrodynamic Equations with Inhomogeneous Boundary Condition

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 44
Author(s):  
Igor Kondrashuk ◽  
Eduardo Alfonso Notte-Cuello ◽  
Mariano Poblete-Cantellano ◽  
Marko Antonio Rojas-Medar
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Compactness Arguments ◽  
Time Periodic ◽  
The Magnetic Field

We show, using the spectral Galerkin method together with compactness arguments, the existence and uniqueness of the periodic strong solutions for the magnetohydrodynamic-type equations with inhomogeneous boundary conditions. Furthermore, we study the asymptotic stability for the time periodic solution for this system. In particular, when the magnetic field h ( x , t ) is zero, we obtain the existence, uniqueness, and asymptotic behavior of the strong solutions to the Navier–Stokes equations with inhomogeneous boundary conditions.

scholarly journals Time periodic Navier–Stokes equations in a thin tube structure

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
R. Juodagalvytė ◽  
G. Panasenko ◽  
K. Pileckas
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Thin Tube ◽  
Time Periodic ◽  
Tube Structure

scholarly journals The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Wen-Juan Wang ◽  
Yan Jia
Keyword(s):  
Weak Solution ◽  
Asymptotic Stability ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Perturbed System ◽  
Regular Class ◽  
Stability Issue ◽  
The Stability

We study the stability issue of the generalized 3D Navier-Stokes equations. It is shown that if the weak solutionuof the Navier-Stokes equations lies in the regular class∇u∈Lp(0,∞;Bq,∞0(ℝ3)),(2α/p)+(3/q)=2α,2<q<∞,0<α<1, then every weak solutionv(x,t)of the perturbed system converges asymptotically tou(x,t)asvt-utL2→0,t→∞.

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