Carleman estimate for the Navier–Stokes equations and an application to a lateral Cauchy problem
Carleman estimate for the Navier–Stokes equations and an application to a lateral Cauchy problem
复制标题
纳维-斯托克斯方程的卡勒曼估计及其在横向柯西问题中的应用
DOI：
10.1088/0266-5611/32/2/025001
复制
发表时间：
2015
期刊：
影响因子：
2.1
通讯作者：
Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
M. Bellassoued;O. Imanuvilov;Masahiro Yamamoto
考虑有界域上的非平稳线性化Navier-Stokes方程，首先用正则权函数证明了Carleman估计。其次，我们将Carleman估计应用于Navier-Stokes方程的侧向Cauchy问题，并证明了在确定内域速度和压力场时Hölder的稳定性。最后，我们将线性化Navier-Stokes方程的结果应用到完全非线性Navier-Stokes方程中，在充分光滑解内建立了类似的Hölder稳定性估计，并在任意选择的子边界上证明了表面应力对Leray-Hopf弱解的唯一性。
We consider the nonstationary linearized Navier–Stokes equations in a bounded domain and first we prove a Carleman estimate with a regular weight function. Second we apply the Carleman estimate to a lateral Cauchy problem for the Navier–Stokes equations and prove the Hölder stability in determining the velocity and pressure field in an interior domain. In the final section, we apply the results for the linearized Navier–Stokes equations to the fully nonlinear Navier–Stokes equations and establish a similar Hölder stability estimate within sufficiently smooth solutions, and prove the uniqueness of Leray–Hopf weak solutions by surface stresses on an arbitrarily chosen sub-boundary.