New results of general \(n\)-dimensional incompressible Navier-Stokes equations
type: Item
instance of: scholarly article
title: New results of general \(n\)-dimensional incompressible Navier-Stokes equations
zbMATH Open document ID: 1157.35084
author: Linghai Zhang
published in: Journal of Differential Equations
publication date: 2008-12-12T00:00:00Z
review text: The Cauchy problem for the general \(n\)-dimensional incompressible Navier-Stokes equations, with arbitrarily large initial data is considered in the whole space. The problem depends on a small parameter \(\varepsilon\), which multiplies the dispersion term. The paper deals with the exact limit of some \(L^2\)-norms of the global strong/weak solutions of the considered problem. For \(\varepsilon=0\), the mathematical analysis provided in this paper is formal and it is done in the sense of tempered distributions, while for \(\varepsilon>0\) the results are rigorous. By taking the initial data of a special form, the limits of physical quantities, as the time tends to \(\infty\), are established. These results suggest that after a long time, the solutions of the considered problem become closer and closer to the solutions of the linearized equation.
reviewed by: Ruxandra Stavre
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 5382317
zbMATH Keywords: exact limits
zbMATH Keywords: optimal rate of decay
zbMATH Keywords: general Navier-Stokes equations
zbMATH Keywords: Cauchy problems
zbMATH Keywords: global solutions
MaRDI profile type: Publication
full work available at URL: j.jde.2008.04.016
OpenAlex ID: W2022506384
cites work: Q4003101
cites work: Q3736200
cites work: \(L^ p\)-stability for the strong solutions of the Navier-Stokes equations in the whole space
cites work: On the smoothness of a class of weak solutions to the Navier-Stokes equations
cites work: Time-periodic solutions of the Navier-Stokes equations in unbounded cylindrical domains-Leray's problem for periodic flows
cites work: Partial regularity of suitable weak solutions of the navier-stokes equations
cites work: Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models
cites work: Large-Time Behavior in Incompressible Navier–Stokes Equations
cites work: Invariant manifolds for flows in Banach spaces
cites work: Integral manifolds and inertial manifolds for dissipative partial differential equations
cites work: Q4851736
cites work: Q3026605
cites work: Finite fractal dimension and Holder-Lipshitz parametrization
cites work: Q3719159
cites work: Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations
cites work: Q4255465
cites work: Q4039920
cites work: Attractors for the two-dimensional Navier--Stokes-\({\alpha}\) model: an \({\alpha}\)-dependence study
cites work: Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
cites work: Strong solutions of the Navier-Stokes equation in Morrey spaces
cites work: The Navier-Stokes equation for an incompressible fluid in \(\mathbb{R}^ 2\) with a measure as the initial vorticity
cites work: A new proof of the Caffarelli-Kohn-Nirenberg theorem
cites work: On optimal decay rates for weak solutions to the Navier-Stokes equations in \(\mathbb R^n\)
cites work: On Leray's self-similar solutions of the Navier-Stokes equations
cites work: Remark on the rate of decay of higher order derivatives for solutions to the Navier-Stokes equations in \(\mathbb{R}^n\)
cites work: \(L^ 2\) decay for weak solutions of the Navier-Stokes equations
cites work: Large time behaviour of solutions to the navier-stokes equations
cites work: Lower Bounds of Rates of Decay for Solutions to the Navier-Stokes Equations
cites work: Global attractors for the three-dimensional Navier-Stokes equations
cites work: On the interior regularity of weak solutions of the Navier-Stokes equations
cites work: Q5723392
cites work: Q5607484
cites work: Q3861771
cites work: Q3672342
cites work: Q3779875
cites work: Infinite-dimensional dynamical systems in mechanics and physics
cites work: Decay Results for Weak Solutions of the Navier-Stokes Equations on Rn
cites work: Q3351840
cites work: Decay of the \(L_ \infty\)-norm of solutions of Navier-Stokes equations in unbounded domains
cites work: Q4286644
cites work: Sharp Rate of Decay of Solutions to 2-Dimensional Navier-Stokes Equations
cites work: Q4949655
cites work: Q4653237
cites work: Solutions to some open problems in fluid dynamics
DOI: 10.1016/J.JDE.2008.04.016
description: scientific article; zbMATH DE number 5382317