论文标题
Navier-Stokes方程与身体力量衰减相干
The Navier-Stokes equations with body forces decaying coherently in time
论文作者
论文摘要
研究了周期域中的三维纳维尔方程的解决方案的长期行为。随着时间$ t $的时间趋向于无限的时间，体力衰减。实际上，假定它具有一般且复杂的渐近扩展，涉及$ e^t $，$ t $，$ \ ln t $的复杂功率或其他$ t $的对数功能。我们证明，所有Leray-Hopf弱解决方案都允许渐近扩张，该膨胀与溶液无关，并由体力的渐近扩张来唯一确定。证明是利用Gevrey-Sobolev空间以及Stokes Operator和Navier-Stokes方程的双线性形式的复杂性。
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 $e^t$, $t$, $\ln t$, 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.
