QUANTITATIVE ESTIMATES FOR SPACE-TIME ANALYTICITY OF SOLUTIONS TO THE FRACTIONAL NAVIER-STOKES EQUATIONS

Cong Wang; Yu Gao; Xiaoping Xue

doi:10.3934/cpaa.2023080

QUANTITATIVE ESTIMATES FOR SPACE-TIME ANALYTICITY OF SOLUTIONS TO THE FRACTIONAL NAVIER-STOKES EQUATIONS

Cong Wang
, Yu Gao
, Xiaoping Xue^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology
Hong Kong Polytechnic University

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

2 Scopus citations

Abstract

We show the optimal decay rate estimates of the space-time derivatives of solutions to the fractional Navier-Stokes equations, which yields the joint space-time analyticity. Consequently, the lower bounds on the growth rate (in time) of radius of space analyticity, time analyticity, and joint space-time analyticity of solutions are obtained. The proofs only involve real variable methods.

Original language	English
Pages (from-to)	2619-2645
Number of pages	27
Journal	Communications on Pure and Applied Analysis
Volume	22
Issue number	8
DOIs	https://doi.org/10.3934/cpaa.2023080
State	Published - 2023
Externally published	Yes

Keywords

Critical space
analytic radius
bootstrapping method
instantaneous regularity
mild solution

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title = "QUANTITATIVE ESTIMATES FOR SPACE-TIME ANALYTICITY OF SOLUTIONS TO THE FRACTIONAL NAVIER-STOKES EQUATIONS",

abstract = "We show the optimal decay rate estimates of the space-time derivatives of solutions to the fractional Navier-Stokes equations, which yields the joint space-time analyticity. Consequently, the lower bounds on the growth rate (in time) of radius of space analyticity, time analyticity, and joint space-time analyticity of solutions are obtained. The proofs only involve real variable methods.",

keywords = "Critical space, analytic radius, bootstrapping method, instantaneous regularity, mild solution",

author = "Cong Wang and Yu Gao and Xiaoping Xue",

year = "2023",

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AU - Wang, Cong

AU - Gao, Yu

AU - Xue, Xiaoping

PY - 2023

Y1 - 2023

N2 - We show the optimal decay rate estimates of the space-time derivatives of solutions to the fractional Navier-Stokes equations, which yields the joint space-time analyticity. Consequently, the lower bounds on the growth rate (in time) of radius of space analyticity, time analyticity, and joint space-time analyticity of solutions are obtained. The proofs only involve real variable methods.

AB - We show the optimal decay rate estimates of the space-time derivatives of solutions to the fractional Navier-Stokes equations, which yields the joint space-time analyticity. Consequently, the lower bounds on the growth rate (in time) of radius of space analyticity, time analyticity, and joint space-time analyticity of solutions are obtained. The proofs only involve real variable methods.

KW - Critical space

KW - analytic radius

KW - bootstrapping method

KW - instantaneous regularity

KW - mild solution

UR - https://www.scopus.com/pages/publications/85174822265

U2 - 10.3934/cpaa.2023080

DO - 10.3934/cpaa.2023080

M3 - 文章

AN - SCOPUS:85174822265

SN - 1534-0392

VL - 22

SP - 2619

EP - 2645

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 8

ER -

QUANTITATIVE ESTIMATES FOR SPACE-TIME ANALYTICITY OF SOLUTIONS TO THE FRACTIONAL NAVIER-STOKES EQUATIONS

Abstract

Keywords

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