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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله

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
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 32, Issue 2, March–April 2015, Pages 347–371
نویسندگان
Luc Molinet, Didier Pilod,