Well-Posedness for the Cauchy Problem for a System of Semirelativistic Equations

被引：3

作者：

Fujiwara, Kazumasa ^{[1
]}

Machihara, Shuji ^{[2
]}

Ozawa, Tohru ^{[3
]}

机构：

[1] Waseda Univ, Dept Pure & Appl Phys, Shinjuku Ku, Tokyo 1698555, Japan

[2] Saitama Univ, Fac Sci, Saitama 3388570, Japan

[3] Waseda Univ, Dept Appl Phys, Shinjuku Ku, Tokyo 1698555, Japan

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2015年 / 338卷 / 01期

关键词：

NONLINEAR SCHRODINGER-EQUATIONS; REGULARITY;

D O I：

10.1007/s00220-015-2347-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The local well-posedness for the Cauchy problem of a system of semirelativistic equations in one space dimension is shown in the Sobolev space H-s of order s >= 0. We apply the standard contraction mapping theorem by using Bourgain type spaces X-s,X-b. We also use an auxiliary space for the solution in L-2 = H-0. We give the global well-posedness by this conservation law and the argument of the persistence of regularity.

引用

页码：367 / 391

页数：25

共 50 条

[1] Well-Posedness for the Cauchy Problem for a System of Semirelativistic Equations
Kazumasa Fujiwara
Shuji Machihara
Tohru Ozawa
Communications in Mathematical Physics, 2015, 338 : 367 - 391
[2] On the Well-Posedness of the Cauchy Problem for the Generalized Telegraph Equations
Kostin, V. A.
Kostin, A. V.
Salim, Badran Yasim Salim
BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE, 2014, 7 (03): : 50 - 59
[3] Well-posedness of the Cauchy problem for the coupled system of the Schrodinger-KdV equations
Guo, BL
Miao, CX
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 1999, 15 (02): : 215 - 224
[4] Well-Posedness of the Cauchy Problem for the Coupled System of the Schrodinger-KdV Equations
Boling Guo
Changxing Miao
ActaMathematicaSinica(EnglishSeries), 1999, 15 (02) : 215 - 224
[5] Well-posedness of the Cauchy problem for the fractional power dissipative equations
Miao, Changxing
Yuan, Baoquan
Zhang, Bo
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (03) : 461 - 484
[6] Well-Posedness of the Cauchy Problem for Stochastic Evolution Functional Equations
M. M. Vas’kovskii
Differential Equations, 2018, 54 : 775 - 789
[7] Well-posedness of the Cauchy problem for p-evolution equations
Ascanelli, Alessia
Boiti, Chiara
Zanghirati, Luisa
JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (10) : 2765 - 2795
[8] Well-Posedness of the Cauchy Problem for Stochastic Evolution Functional Equations
Vas'kovskii, M. M.
DIFFERENTIAL EQUATIONS, 2018, 54 (06) : 775 - 789
[9] Well-posedness of the cauchy problem for an inclusion
I. V. Mel’nikova
Differential Equations, 2004, 40 : 1512 - 1516
[10] Well-posedness of the cauchy problem for an inclusion
I. V. Mel’nikova
Differential Equations, 2004, 40 : 1512 - 1516

← 1 2 3 4 5 →