کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772235 | 1413353 | 2017 | 74 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Symplectic non-squeezing for the cubic nonlinear Klein-Gordon equation on T3
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Symplectic non-squeezing for the cubic nonlinear Klein-Gordon equation on T3 Symplectic non-squeezing for the cubic nonlinear Klein-Gordon equation on T3](/preview/png/5772235.png)
چکیده انگلیسی
We consider the periodic defocusing cubic nonlinear Klein-Gordon equation in three dimensions in the symplectic phase space H12(T3)ÃHâ12(T3). This space is at the critical regularity for this equation, and in this setting there is no global well-posedness nor any uniform control on the local time of existence for arbitrary initial data. We prove a local-in-time non-squeezing result and a conditional global-in-time result which states that uniform bounds on the Strichartz norms of solutions imply global-in-time non-squeezing. As an application of the conditional result, we conclude non-squeezing for certain subsets of the phase space. The proofs rely on several approximation results for the flow, which we obtain using a combination of probabilistic and deterministic techniques.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 272, Issue 7, 1 April 2017, Pages 3019-3092
Journal: Journal of Functional Analysis - Volume 272, Issue 7, 1 April 2017, Pages 3019-3092
نویسندگان
Dana Mendelson,