Remark on the Lifespan of Solutions to 3-D Anisotropic Navier Stokes Equations

Liang, Siyu

doi:10.4208/cmr.2020-0002

Cited by 5 publications

(3 citation statements)

References 12 publications

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“…One may check [10] and the references therein for details concerning the well-posedness theory of (1.1). The authors of [11] studied the lower bound to the lifespan of the local smooth solutions to the system (1.1).…”

Section: Introductionmentioning

confidence: 99%

Enhanced dissipation for the third component of 3D anisotropic Navier-Stokes equations

Xu¹,

Zhang²

2021

Preprint

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In this paper, we study the decay rates for the global small smooth solutions to 3D anisotropic incompressible Navier-Stokes equations. In particular, we prove that the horizontal components of the velocity field decay like the solutions of 2D classical Navier-Stokes equations. While the third component of the velocity field decays as the solutions of 3D Navier-Stokes equations. We remark that such enhanced decay rate for the third component is caused by the interplay between the divergence free condition of the velocity field and the horizontal Laplacian in the anisotropic Navier-Stokes equations.

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Section: Introductionmentioning

confidence: 99%

Enhanced dissipation for the third component of 3D anisotropic Navier-Stokes equations

Xu¹,

Zhang²

2021

Preprint

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“…We refer the readers to [3,5,9,15] for well-posedness of (1.8) in other functional spaces. However, there seems little work concerning the lifespan of this anisotropic system (1.8) except [11]. And our result states as follows:…”

Section: Introductionmentioning

confidence: 58%

The influence of viscous coefficients on the lifespan of 3-D anisotropic Navier-Stokes system

Hao¹,

Liu²

2021

Preprint

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The anisotropic Navier-Stokes system arises in geophysical fluid dynamics, which is derived by changing −ν∆ in the classical Navier-Stokes system to −(ν1∂ 2 1 + ν2∂ 2 2 + ν3∂ 2 3 ). Here ν1, ν2 , ν3 are the viscous coefficients, which can be different from each other. This reflects that the fluid can behave differently in each direction.The purpose of this paper is to derive some lower bound estimates on the lifespan to such anisotropic Navier-Stokes system. We not only investigate the case when ν1, ν2 , ν3 are all positive, but also the more sophisticated cases when one or two of them vanish. We find that in these lower bound estimates, the weights of ν1, ν2 , ν3 are not equal. A detailed study of this problem can also help us to have a better understanding of the nonlinear structure in the classical Navier-Stokes system.

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“…In other words, it is a strong solution up to time T . For deterministic anisotropic 3D Navier-Stokes equations, in [5], we also study the maximal time up to which the solutions remain regular.…”

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confidence: 99%

A Lower Bound Estimate of Life Span of Solutions to Stochastic 3D Navier-Stokes Equations with Convolution Type Noise

Liang¹

2021

Preprint

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Remark on the Lifespan of Solutions to 3-D Anisotropic Navier Stokes Equations

Abstract: The goal of this article is to provide a lower bound for the lifespan of smooth solutions to 3-D anisotropic incompressible Navier-Stokes system, which in particular extends a similar type of result for the classical 3-D incompressible Navier-Stokes system.

Cited by 5 publications

References 12 publications

Enhanced dissipation for the third component of 3D anisotropic Navier-Stokes equations

Enhanced dissipation for the third component of 3D anisotropic Navier-Stokes equations

The influence of viscous coefficients on the lifespan of 3-D anisotropic Navier-Stokes system

A Lower Bound Estimate of Life Span of Solutions to Stochastic 3D Navier-Stokes Equations with Convolution Type Noise

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