TY - JOUR

T1 - The Navier–Stokes equations with body forces decaying coherently in time

AU - Hoang, Luan

N1 - Publisher Copyright:
© 2023 Elsevier Inc.

PY - 2024/3/15

Y1 - 2024/3/15

N2 - The long-time behavior of solutions of the three-dimensional Navier–Stokes equations in a periodic domain is studied. The time-dependent body force decays, as time t tends to infinity, in a coherent manner. In fact, it is assumed to have a general and complicated asymptotic expansion which involves complex powers of et, t, lnt, or other iterated logarithmic functions of t. We prove that all Leray–Hopf weak solutions admit an asymptotic expansion which is independent of the solutions and is uniquely determined by the asymptotic expansion of the body force. The proof makes use of the complexifications of the Gevrey–Sobolev spaces together with those of the Stokes operator and the bilinear form of the Navier–Stokes equations.

AB - The long-time behavior of solutions of the three-dimensional Navier–Stokes equations in a periodic domain is studied. The time-dependent body force decays, as time t tends to infinity, in a coherent manner. In fact, it is assumed to have a general and complicated asymptotic expansion which involves complex powers of et, t, lnt, or other iterated logarithmic functions of t. We prove that all Leray–Hopf weak solutions admit an asymptotic expansion which is independent of the solutions and is uniquely determined by the asymptotic expansion of the body force. The proof makes use of the complexifications of the Gevrey–Sobolev spaces together with those of the Stokes operator and the bilinear form of the Navier–Stokes equations.

KW - Asymptotic expansions

KW - Complicated expansions

KW - Fluid dynamics

KW - Long-time behavior

KW - Navier–Stokes equations

UR - http://www.scopus.com/inward/record.url?scp=85174459358&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2023.127863

DO - 10.1016/j.jmaa.2023.127863

M3 - Article

AN - SCOPUS:85174459358

SN - 0022-247X

VL - 531

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 127863

ER -