WELL-POSEDNESS AND PARABOLIC SMOOTHING EFFECT FOR HIGHER ORDER SCHRONDINGER TYPE EQUATIONS WITH CONSTANT COEFFICIENTS

被引：0

作者：

Tanaka, Tomoyuki ^{[1
]}

Tsugawa, Kotaro ^{[2
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

[2] Chuo Univ, Fac Sci & Engn, Dept Math, Bunkyo Ku, Tokyo 1128551, Japan

来源：

OSAKA JOURNAL OF MATHEMATICS | 2022年 / 59卷 / 02期

关键词：

INITIAL-VALUE PROBLEM; CAUCHY-PROBLEM;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the Cauchy problem of a class of higher order Schrodinger type equations with constant coefficients. By employing the energy inequality, we show the L-2 well-posedness, the parabolic smoothing and a breakdown of the persistence of regularity. We classify this class of equations into three types on the basis of their smoothing property.

引用

页码：465 / 480

页数：16

共 21 条

[1] A SHARP CONDITION FOR THE WELL-POSEDNESS OF THE LINEAR KDV-TYPE EQUATION
Akhunov, Timur
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (12) : 4207 - 4220
[2] The initial value problem for Schrodinger equations on the torus
Chihara, H
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2002, 2002 (15) : 789 - 820
[3] Doi S, 1996, COMMUN PART DIFF EQ, V21, P163
[4] On the hierarchies of higher order mKdV and KdV equations
Gruenrock, Axel
[J]. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2010, 8 (03): : 500 - 536
[5] ON THE DERIVATIVE NONLINEAR SCHRODINGER-EQUATION
HAYASHI, N
OZAWA, T
[J]. PHYSICA D, 1992, 55 (1-2): : 14 - 36
[6] THE INITIAL-VALUE PROBLEM FOR THE DERIVATIVE NONLINEAR SCHRODINGER-EQUATION IN THE ENERGY SPACE
HAYASHI, N
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1993, 20 (07) : 823 - 833
[7] LONG TIME SOLUTIONS FOR A BURGERS-HILBERT EQUATION VIA A MODIFIED ENERGY METHOD
Hunter, John K.
Ifrim, Mihaela
Tataru, Daniel
Wong, Tak Kwong
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 143 (08) : 3407 - 3412
[8] ICHINOSE W, 1984, OSAKA J MATH, V21, P565
[9] The Cauchy problem for Schrodinger type equations with variable coefficients
Kajitani, K
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1998, 50 (01) : 179 - 202
[10] Kenig CE, 2016, ADV DIFFERENTIAL EQU, V21, P801

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