کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4604127 1337418 2015 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bilinear Strichartz estimates for the Zakharov–Kuznetsov equation and applications
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Bilinear Strichartz estimates for the Zakharov–Kuznetsov equation and applications
چکیده انگلیسی

This article is concerned with the Zakharov–Kuznetsov equationequation(0.1)∂tu+∂xΔu+u∂xu=0.∂tu+∂xΔu+u∂xu=0. We prove that the associated initial value problem is locally well-posed in Hs(R2)Hs(R2) for s>12 and globally well-posed in H1(R×T)H1(R×T) and in Hs(R3)Hs(R3) for s>1s>1. Our main new ingredient is a bilinear Strichartz estimate in the context of Bourgain's spaces which allows to control the high-low frequency interactions appearing in the nonlinearity of (0.1). In the R2R2 case, we also need to use a recent result by Carbery, Kenig and Ziesler on sharp Strichartz estimates for homogeneous dispersive operators. Finally, to prove the global well-posedness result in R3R3, we need to use the atomic spaces introduced by Koch and Tataru.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 32, Issue 2, March–April 2015, Pages 347–371
نویسندگان
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