Hokkaido Mathematical Journal

Spatial Asymptotic Profiles of Solutions to the Navier-Stokes System in a Rotating Frame with Fast Decaying Data

Reinhard FARWIG, Raphael SCHULZ, and Yasushi TANIUCHI

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Abstract

The nonstationary Navier-Stokes system for a viscous, incompressible fluid influenced by a Coriolis force in the whole space ${\mathbb R}^3$ is considered at large distances. The solvability of the corresponding integral equations of these equations in weighted $L^\infty$-spaces is established. Furthermore, the leading terms of the asymptotic profile of the solution at fixed time $t \gt 0$ for $|x| \gt t$ and far from the axis of rotation are investigated.

Article information

Source
Hokkaido Math. J., Volume 47, Number 3 (2018), 501-529.

Dates
First available in Project Euclid: 26 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1537948828

Digital Object Identifier
doi:10.14492/hokmj/1537948828

Mathematical Reviews number (MathSciNet)
MR3858376

Zentralblatt MATH identifier
06959101

Subjects
Primary: 76U05: Rotating fluids
Secondary: 76D05: Navier-Stokes equations [See also 35Q30] 35B40: Asymptotic behavior of solutions 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 35Q35: PDEs in connection with fluid mechanics

Keywords
Rotating Navier-Stokes equations Coriolis operator mild solutions weighted $L^\infty$-spaces rate of spatial decay

Citation

FARWIG, Reinhard; SCHULZ, Raphael; TANIUCHI, Yasushi. Spatial Asymptotic Profiles of Solutions to the Navier-Stokes System in a Rotating Frame with Fast Decaying Data. Hokkaido Math. J. 47 (2018), no. 3, 501--529. doi:10.14492/hokmj/1537948828. https://projecteuclid.org/euclid.hokmj/1537948828


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