Global Small Analytic Solution of 3-D Anisotropic Navier-Stokes System

Ning Liu; Ping Zhang

doi:10.1007/s00205-024-02051-2

Global Small Analytic Solution of 3-D Anisotropic Navier-Stokes System

Ning Liu
, Ping Zhang

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we prove the global existence of analytic solution for 3D anisotropic Navier-Stokes system with initial data which is small and analytic in the vertical variable. We shall also prove that this solution will be analytic in the horizontal variables soon after t>0. Furthermore, we show that the ratio between the analytic radius, R_h(t), of the solution in the horizontal variables and t satisfies lim_{_t_→0₊}R_h(t)t=∞.

Original language	English
Article number	106
Journal	Archive for Rational Mechanics and Analysis
Volume	248
Issue number	6
DOIs	https://doi.org/10.1007/s00205-024-02051-2
Publication status	Published - Dec 2024
Externally published	Yes

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10.1007/s00205-024-02051-2

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title = "Global Small Analytic Solution of 3-D Anisotropic Navier-Stokes System",

abstract = "In this paper, we prove the global existence of analytic solution for 3D anisotropic Navier-Stokes system with initial data which is small and analytic in the vertical variable. We shall also prove that this solution will be analytic in the horizontal variables soon after t>0. Furthermore, we show that the ratio between the analytic radius, Rh(t), of the solution in the horizontal variables and t satisfies limt→0+Rh(t)t=∞.",

author = "Ning Liu and Ping Zhang",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.",

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N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

PY - 2024/12

Y1 - 2024/12

N2 - In this paper, we prove the global existence of analytic solution for 3D anisotropic Navier-Stokes system with initial data which is small and analytic in the vertical variable. We shall also prove that this solution will be analytic in the horizontal variables soon after t>0. Furthermore, we show that the ratio between the analytic radius, Rh(t), of the solution in the horizontal variables and t satisfies limt→0+Rh(t)t=∞.

AB - In this paper, we prove the global existence of analytic solution for 3D anisotropic Navier-Stokes system with initial data which is small and analytic in the vertical variable. We shall also prove that this solution will be analytic in the horizontal variables soon after t>0. Furthermore, we show that the ratio between the analytic radius, Rh(t), of the solution in the horizontal variables and t satisfies limt→0+Rh(t)t=∞.

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Global Small Analytic Solution of 3-D Anisotropic Navier-Stokes System

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