scholarly journals A local Fourier analysis of additive Vanka relaxation for the Stokes equations

2020 ◽  
Author(s):  
Patrick E. Farrell ◽  
Yunhui He ◽  
Scott P. MacLachlan
Keyword(s):  
Fourier Analysis ◽  
Stokes Equations ◽  
Local Fourier Analysis

scholarly journals Remarks on the Systems of Semilinear Fractional Rayleigh-Stokes Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Le Dinh Long
Keyword(s):  
Cauchy Problem ◽  
Fourier Analysis ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Newtonian Fluids ◽  
System Of Equations ◽  
Main Technique ◽  
The Cauchy Problem ◽  
The Stability

In this paper, we study the Cauchy problem for a system of Rayleigh-Stokes equations. In this system of equations, we use derivatives in the classical Riemann-Liouville sense. This system has many applications in some non-Newtonian fluids. We obtained results for the existence, uniqueness, and frequency of the solution. We discuss the stability of the solutions and find the solution spaces. Our main technique is to use the Banach mapping theorem combined with some techniques in Fourier analysis.

scholarly journals On Local Fourier Analysis of Multigrid Methods for PDEs with Jumping and Random Coefficients

2019 ◽  
Vol 41 (3) ◽  
pp. A1385-A1413 ◽  
Author(s):  
Prashant Kumar ◽  
Carmen Rodrigo ◽  
Francisco J. Gaspar ◽  
Cornelis W. Oosterlee
Keyword(s):  
Fourier Analysis ◽  
Multigrid Methods ◽  
Random Coefficients ◽  
Local Fourier Analysis

scholarly journals Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces

2021 ◽  
Vol 19 (1) ◽  
pp. 898-908
Author(s):  
Lotfi Jlali
Keyword(s):  
Fourier Analysis ◽  
Global Solution ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Decay ◽  
Navier Stokes Equations ◽  
Long Time

Abstract In this paper, we study the long time decay of global solution to the 3D incompressible Navier-Stokes equations. We prove that if u ∈ C ( R + , X − 1 , σ ( R 3 ) ) u\in {\mathcal{C}}\left({{\mathbb{R}}}^{+},{{\mathcal{X}}}^{-1,\sigma }\left({{\mathbb{R}}}^{3})) is a global solution to the considered equation, where X i , σ ( R 3 ) {{\mathcal{X}}}^{i,\sigma }\left({{\mathbb{R}}}^{3}) is the Fourier-Lei-Lin space with parameters i = − 1 i=-1 and σ ≥ − 1 \sigma \ge -1 , then ‖ u ( t ) ‖ X − 1 , σ \Vert u\left(t){\Vert }_{{{\mathcal{X}}}^{-1,\sigma }} decays to zero as time goes to infinity. The used techniques are based on Fourier analysis.

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