کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6419493 1339410 2011 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Reducing slip boundary value problems from the half to the whole space. Applications to inviscid limits and to non-Newtonian fluids
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Reducing slip boundary value problems from the half to the whole space. Applications to inviscid limits and to non-Newtonian fluids
چکیده انگلیسی

The study of a very large class of linear and non-linear, stationary and evolutive partial differential problems in the half-space (or similar) under the slip boundary condition is reduced here to the much simpler study of the corresponding results for the same problem in the whole space. The approach is particularly suitable for proving new results in strong norms. To determine whether this extension is available, turns out to be a simple exercise. The verification depends on a few general features of the functional space X related to the space variables. Hence, we present an approach as much as possible independent of the particular space X. We appeal to a reflection technique. Hence a crucial assumption is to be in the presence of flat boundaries (see below). Instead of stating “general theorems” we rather prefer to illustrate how to apply our results by considering a couple of interesting problems. As a main example, we show that sharp vanishing viscosity limit results that hold for the evolution Navier-Stokes equations in the whole space can be extended to the slip boundary value problem in the half-space. We also show some applications to non-Newtonian fluid problems.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 377, Issue 1, 1 May 2011, Pages 216-227
نویسندگان
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