论文标题
定期LP估算通过R-BONDEDES：NAVIER-Stokes方程的应用
Periodic Lp estimates by R-boundedness: Applications to the Navier-Stokes equations
论文作者
论文摘要
研究了Banach空间中的一般进化方程。基于De Leeuw的转移原则的操作员值，最大规则性类型的时间周期性$ l^p $估计值是从$ \ Mathscr {r} $ - 解决方案操作员家族（$ \ MATHSCR {r} $ - solvers）的界限到相应的Resolvent问题。通过这种方法，显示了两种配置的Navier-Stokes方程的时间周期解决方案：在定期移动的有界域和外部域中，以规定的时间周期强迫和边界数据为生。
General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw's transference principle, time-periodic $L^p$ estimates of maximal regularity type are established from $\mathscr{R}$-bounds of the family of solution operators ($\mathscr{R}$-solvers) to the corresponding resolvent problems. With this method, existence of time-periodic solutions to the Navier-Stokes equations is shown for two configurations: in a periodically moving bounded domain and in an exterior domain, subject to prescribed time-periodic forcing and boundary data.
