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Analytic semigroup approach to generalized Navier-Stokes flows in Besov spaces

Analytic semigroup approach to generalized Navier-Stokes flows in Besov spaces
Analytic semigroup approach to generalized Navier-Stokes flows in Besov spaces
The energy dissipation of the Navier-Stokes equations is controlled by the viscous force defined by the Laplacian -Delta, while that of the generalized Navier-Stokes equations is determined by the fractional Laplacian (-Delta)^\alpha. The existence and uniqueness problem is always solvable in a strong dissipation situation in the sense of large alpha but it becomes complicated when alpha is decreasing. In this paper, the well-posedness regarding to the unique existence of small time solutions and small initial data solutions is examined in critical homogeneous Besov spaces for alpha >= 1/2. An analytic semigroup approach to the understanding of the generalized Navier-Stokes equations is developed and thus the well-posedness on the equations is examined in a manner different to earlier investigations.
1422-6928
709-724
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f

Chen, Zhi-Min (2017) Analytic semigroup approach to generalized Navier-Stokes flows in Besov spaces. Journal of Mathematical Fluid Mechanics, 19 (4), 709-724. (doi:10.1007/s00021-016-0302-5).

Record type: Article

Abstract

The energy dissipation of the Navier-Stokes equations is controlled by the viscous force defined by the Laplacian -Delta, while that of the generalized Navier-Stokes equations is determined by the fractional Laplacian (-Delta)^\alpha. The existence and uniqueness problem is always solvable in a strong dissipation situation in the sense of large alpha but it becomes complicated when alpha is decreasing. In this paper, the well-posedness regarding to the unique existence of small time solutions and small initial data solutions is examined in critical homogeneous Besov spaces for alpha >= 1/2. An analytic semigroup approach to the understanding of the generalized Navier-Stokes equations is developed and thus the well-posedness on the equations is examined in a manner different to earlier investigations.

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Semigroup approach to Fractional NS_16Oct16.pdf - Accepted Manuscript
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Accepted/In Press date: 17 October 2016
e-pub ahead of print date: 2 November 2017
Published date: December 2017
Organisations: Fluid Structure Interactions Group

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Local EPrints ID: 401693
URI: https://eprints.soton.ac.uk/id/eprint/401693
ISSN: 1422-6928
PURE UUID: 216db20c-3df8-4d83-aae0-4ef99395460f

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Date deposited: 19 Oct 2016 14:07
Last modified: 19 Jan 2018 05:01

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Author: Zhi-Min Chen

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