کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4604140 | 1337419 | 2016 | 68 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Invariance of the Gibbs measure for the periodic quartic gKdV
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Invariance of the Gibbs measure for the periodic quartic gKdV Invariance of the Gibbs measure for the periodic quartic gKdV](/preview/png/4604140.png)
چکیده انگلیسی
We prove invariance of the Gibbs measure for the (gauge transformed) periodic quartic gKdV. The Gibbs measure is supported on Hs(T)Hs(T) for s<12, and the quartic gKdV is analytically ill-posed in this range. In order to consider the flow in the support of the Gibbs measure, we combine a probabilistic argument with the second iteration and construct local-in-time solutions to the (gauge transformed) quartic gKdV almost surely in the support of the Gibbs measure. Then, we use Bourgain's idea to extend these local solutions to global solutions, and prove the invariance of the Gibbs measure under the flow. Finally, inverting the gauge, we construct almost sure global solutions to the (ungauged) quartic gKdV below H12(T).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 33, Issue 3, May–June 2016, Pages 699–766
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 33, Issue 3, May–June 2016, Pages 699–766
نویسندگان
Geordie Richards,