TY - JOUR

T1 - Long-time asymptotic expansions for Navier-Stokes equations with power-decaying forces

AU - Cao, Dat

AU - Hoang, Luan

N1 - Funding Information:
L.H. gratefully acknowledges the support for his research by the NSF grant DMS-1412796.
Publisher Copyright:
© Copyright Royal Society of Edinburgh 2019.

PY - 2020/4/1

Y1 - 2020/4/1

N2 - The Navier-Stokes equations for viscous, incompressible fluids are studied in the three-dimensional periodic domains, with the body force having an asymptotic expansion, when time goes to infinity, in terms of power-decaying functions in a Sobolev-Gevrey space. Any Leray-Hopf weak solution is proved to have an asymptotic expansion of the same type in the same space, which is uniquely determined by the force, and independent of the individual solutions. In case the expansion is convergent, we show that the next asymptotic approximation for the solution must be an exponential decay. Furthermore, the convergence of the expansion and the range of its coefficients, as the force varies are investigated.

AB - The Navier-Stokes equations for viscous, incompressible fluids are studied in the three-dimensional periodic domains, with the body force having an asymptotic expansion, when time goes to infinity, in terms of power-decaying functions in a Sobolev-Gevrey space. Any Leray-Hopf weak solution is proved to have an asymptotic expansion of the same type in the same space, which is uniquely determined by the force, and independent of the individual solutions. In case the expansion is convergent, we show that the next asymptotic approximation for the solution must be an exponential decay. Furthermore, the convergence of the expansion and the range of its coefficients, as the force varies are investigated.

KW - Navier-Stokes

KW - asymptotic expansion

KW - power-decaying

UR - http://www.scopus.com/inward/record.url?scp=85060367644&partnerID=8YFLogxK

U2 - 10.1017/prm.2018.154

DO - 10.1017/prm.2018.154

M3 - Article

AN - SCOPUS:85060367644

VL - 150

SP - 569

EP - 606

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 2

ER -