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.
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页码：661 / 678
页数：18
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