کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5774093 | 1413544 | 2017 | 53 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Convergence rates and W1,p estimates in homogenization theory of Stokes systems in Lipschitz domains
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Concerned with the Stokes systems with rapidly oscillating periodic coefficients, we mainly extend the recent works in [19], [20] to those in term of Lipschitz domains. The arguments employed here are quite different from theirs, and the basic idea comes from [37], originally motivated by [23], [27], [33]. We obtain an almost-sharp O(εlnâ¡(r0/ε)) convergence rate in L2 space, and a sharp O(ε) error estimate in L2ddâ1 space by a little stronger assumption. Under the dimensional condition d=2, we also establish the optimal O(ε) convergence rate on pressure terms in L2 space. Then utilizing the convergence rates we can derive the W1,p estimates uniformly down to microscopic scale ε without any smoothness assumption on the coefficients, where |1pâ12|<12d+ϵ and ϵ is a positive constant independent of ε. Combining the local estimates, based upon VMO coefficients, consequently leads to the uniform W1,p estimates. Here the proofs do not rely on the well known compactness methods.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 263, Issue 1, 5 July 2017, Pages 398-450
Journal: Journal of Differential Equations - Volume 263, Issue 1, 5 July 2017, Pages 398-450
نویسندگان
Qiang Xu,