اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPeriodic homogenization of Greens functions for Stokes systems
73
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This paper is devoted to establishing the uniform estimates and asymptotic behaviors of the Greens functions $(G_varepsilon,Pi_varepsilon)$ (and fundamental solutions $(Gamma_varepsilon, Q_varepsilon)$) for the Stokes system with periodically oscillating coefficients (including a system of linear incompressible elasticity). Particular emphasis will be placed on the new oscillation estimates for the pressure component $Pi_varepsilon$. Also, for the first time we prove the textit{adjustable} uniform estimates (i.e., Lipschitz estimate for velocity and oscillation estimate for pressure) by making full use of the Greens functions. Via these estimates, we establish the asymptotic expansions of $G_varepsilon, abla G_varepsilon, Pi_varepsilon$ and more, with a tiny loss on the errors. Some estimates obtained in this paper are new even for Stokes system with constant coefficients, and possess potential applications in homogenization of Stokes or elasticity system.
قيم البحث
اقرأ أيضاً
We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain $Omegasubset mathbb{R}^d$, where $dge 2$. We construct the Green function when coefficients are merely measurable in one direction and have Dini m
ean oscillation in the other directions, and $Omega$ is such that the divergence equation is solvable there. We also establish global pointwise bounds for the Green function and its derivatives when coefficients have Dini mean oscillation and $Omega$ has a $C^{1,rm{Dini}}$ boundary. Green functions for the flow velocity of Stokes systems are also considered.
This paper is concerned with periodic homogenization of second-order elliptic systems in divergence form with oscillating Dirichlet data or Neumann data of first order. We prove that the homogenized boundary data belong to $W^{1, p}$ for any $1<p<inf
ty$. In particular, this implies that the boundary layer tails are Holder continuous of order $alpha$ for any $alpha in (0,1)$.
We prove the existence and pointwise bounds of the Green functions for stationary Stokes systems with measurable coefficients in two dimensional domains. We also establish pointwise bounds of the derivatives of the Green functions under a regularity
assumption on the $L_1$-mean oscillations of the coefficients.
This work develops a quantitative homogenization theory for random suspensions of rigid particles in a steady Stokes flow, and completes recent qualitative results. More precisely, we establish a large-scale regularity theory for this Stokes problem,
and we prove moment bounds for the associated correctors and optimal estimates on the homogenization error; the latter further requires a quantitative ergodicity assumption on the random suspension. Compared to the corresponding quantitative homogenization theory for divergence-form linear elliptic equations, substantial difficulties arise from the analysis of the fluid incompressibility and the particle rigidity constraints. Our analysis further applies to the problem of stiff inclusions in (compressible or incompressible) linear elasticity and in electrostatics; it is also new in those cases, even in the periodic setting.
This paper is concerned with the regularity theory of a transmission problem arising in composite materials. We give a new self-contained proof for the $C^{k,alpha}$ estimates on both sides of the interface under the minimal assumptions on the interf
ace and data. Moreover, we prove the uniform Lipschitz estimate across a $C^{1,alpha}$ interface when the coefficients on both sides of the interface are periodic with independent structures and oscillating at different microscopic scales.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
