کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
844633 908603 2007 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Mean field equation for equilibrium vortices with neutral orientation
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Mean field equation for equilibrium vortices with neutral orientation
چکیده انگلیسی

This paper is concerned with the equilibrium mean field equation of many vortices of the perfect fluid with neutral orientation, −Δv=λ(ev∫Ωevdx−e−v∫Ωe−vdx) in ΩΩ, v=0v=0 on ∂Ω∂Ω, where Ω⊂R2 is a bounded domain with smooth boundary ∂Ω∂Ω, and λ≥0λ≥0 is a constant.Using the isoperimetric inequality of [T. Suzuki, Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity, Ann. Inst. H. Poincaré 9 (1992) 367–398] and mean value theorem of [T. Suzuki, Semilinear Elliptic Equations, Gakkotosho, Tokyo, 1994], we prove the linear stability and a priori estimate of any solution under some assumptions on the domain and the parameter λλ, which lead to the uniqueness theorem of the trivial solution on a simply connected domain and the calculation of the Leray–Schauder degree on any domain for λλ in a certain range.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 66, Issue 2, 15 January 2007, Pages 509–526
نویسندگان
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