ON THE GROWTH OF HIGH SOBOLEV NORMS OF THE FOURTH-ORDER SCHRO?DINGER EQUATION

被引：1

作者：

Chen, Qionglei ^{[1
]}

Deng, Mingming ^{[2
]}

机构：

[1] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

[2] China Acad Engn Phys, Grad Sch, Beijing 100089, Peoples R China

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2023年 / 36卷 / 7-8期

关键词：

GLOBAL WELL-POSEDNESS; CAUCHY-PROBLEM;

D O I：

10.57262/die036-0708-661

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the Sobolev norm growth for the solution to the one-dimensional cubic fourth-order Schro center dot dinger equa-tion. Applying Tao's [k; Z]-multiplier method, we gain some bilinear estimates. Then we show the solution satisfies parallel to u(t)parallel to Hs <= parallel to u(tau)parallel to Hs + C parallel to u(tau )parallel to 1-delta Hs , delta-1 = (s - 2)+ and then derive a polynomial upper bound of time t.

引用

页码：661 / 678

页数：18

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