کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
7222594 1470428 2018 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An infinite scale of incompressible twisting solutions to the nonlinear elliptic system ℒ[u;A,B]=∇P and the discriminant Δ(h,g)
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
An infinite scale of incompressible twisting solutions to the nonlinear elliptic system ℒ[u;A,B]=∇P and the discriminant Δ(h,g)
چکیده انگلیسی
In this paper we consider the second order nonlinear elliptic system div[A(|x|,|u|2,|∇u|2)∇u]+B(|x|,|u|2,|∇u|2)u=[cof∇u]∇P,where the unknown vector field u satisfies the incompressibility constraint det∇u=1a.e. along with suitable boundary conditions and P=P(x) is an a priori unknown hydrostatic pressure field. Here, A=A(r,s,ξ) and B=B(r,s,ξ) are sufficiently regular scalar functions satisfying natural structural properties. Most notably in the case of a finite symmetric annulus we prove the existence of a countably infinite scale of topologically distinct twisting solutions to the system in all even dimensions. In sharp contrast in odd dimensions the only twisting solution is the map u≡x. We study a related class of systems by introducing the novel notion of a discriminant. Using this a complete and explicit characterisation of all twisting solutions for n≥2 is given and a curious dichotomy in the behaviour of the system and its solutions captured and analysed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis - Volume 173, August 2018, Pages 209-219
نویسندگان
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