Attractor of the limiting Navier--Stokes--Voigt system in \mathbb R⁴

2025/07/04 by Ilyin, Alexei, Kalantarov, Varga, Zelik, Sergey
#35B41 #35Q30 #37L30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.03686

Abstract

The Navier--Stokes--Voigt system in the whole four-dimensional space is considered. Although we do not know any physical reasons to consider this system in space dimension four, the attractors theory for this case becomes especially simple and elegant and nothing similar happens when the space dimension is different than four. These notes are devoted to developing this theory, including well-posedness, dissipativity, existence of a global attractor and estimates for its dimension.

Citations

• Attractors for the Navier--Stokes--Voight equations and their dimension
• Sharp bounds on the attractor dimensions for damped wave equations
• On a class of interpolation inequalities on the 2D sphere
• Applications of the Lieb--Thirring and other bounds for orthonormal systems in mathematical hydrodynamics
• Dimension estimates for the attractor of the regularized damped Euler equations on the sphere
• Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations
• Cwikel's bound reloaded
• Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations
• Global attractors and determining modes for the 3D Navier-Stokes-Voight equations
• The Three Dimensional Viscous Camassa-Holm Equations, and Their Relation to the Navier-Stokes Equations and Turbulence Theory

Related

• Attractors for the Navier--Stokes--Voight equations and their dimension
• Attractors and their dimensions for the 3D Fractional Navier--Stokes--Voigt Equations
• Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations
• On the Attractor for the Semi-Dissipative Boussinesq Equations
• Upper bounds for the attractor dimension of damped Navier-Stokes\n equations in mathbb R²