کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898568 | 1631490 | 2018 | 49 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Small data well-posedness for derivative nonlinear Schrödinger equations
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study the local and global solutions of the generalized derivative nonlinear Schrödinger equation iâtu+Îu=P(u,uâ¾,âxu,âxuâ¾), where each monomial in P is of degree 3 or higher, in low-regularity Sobolev spaces without using a gauge transformation. Instead, we use a solution decomposition technique introduced in [4] during the perturbative argument to deal with the loss on derivative in nonlinearity. It turns out that when each term in P contains only one derivative, the equation is locally well-posed in H12, otherwise we have a local well-posedness in H32. If each monomial in P is of degree 5 or higher, the solution can be extended globally. By restricting to equations to the form iâtu+Îu=âxP(u,uâ¾) with the quintic nonlinearity, we were able to obtain the global well-posedness in the critical Sobolev space.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 265, Issue 8, 15 October 2018, Pages 3792-3840
Journal: Journal of Differential Equations - Volume 265, Issue 8, 15 October 2018, Pages 3792-3840
نویسندگان
Donlapark Pornnopparath,