LOW REGULARITY WELL-POSEDNESS FOR THE YANG-MILLS SYSTEM IN FOURIER-LEBESGUE SPACES

被引：1

作者：

Pecher, Hartmut ^{[1
]}

机构：

[1] Berg Univ Wuppertal, Fak Math & Nat Wissensch, D-42119 Wuppertal, Germany

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2020年 / 52卷 / 04期

关键词：

Yang-Mills; local well-posedness; Lorenz gauge; ENERGY SOLUTIONS; EQUATIONS;

D O I：

10.1137/19M1299530

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Cauchy problem for the Yang-Mills system in three space dimensions with data in Fourier-Lebesgue spaces (H) over cap (s,r), 1 < r <= 2 , is shown to be locally well-posed, where we have to assume only almost optimal minimal regularity for the data with respect to scaling as r -> 1 . This is true despite the fact that no null condition is known for one of the critical quadratic nonlinearities, which by now prevented the corresponding result in the classical case r = 2 with data in standard Sobolev spaces.

引用

页码：3131 / 3148

页数：18

共 18 条

[1]

D'Ancona P, 2012, T AM MATH SOC, V364, P31

[2] Bilinear space-time estimates for homogeneous wave equations [J].

Foschi, D ;

Klainerman, S .

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2000, 33 (02) :211-274

[3] ALMOST CRITICAL WELL-POSEDNESS FOR NONLINEAR WAVE EQUATIONS WITH Qμν NULL FORMS IN 2D [J].

Grigoryan, Viktor ;

Nahmod, Andrea R. .

MATHEMATICAL RESEARCH LETTERS, 2014, 21 (02) :313-332

[4] ON THE WAVE EQUATION WITH QUADRATIC NONLINEARITIES IN THREE SPACE DIMENSIONS [J].

Gruenrock, Axel .

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2011, 8 (01) :1-8

[5]

Grünrock A, 2004, INT MATH RES NOTICES, V2004, P3287

[6]

Grunrock A, 2009, T AM MATH SOC, V361, P5681

[7] Bilinear estimates and applications to nonlinear wave equations [J].

Klainerman, S ;

Selberg, S .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2002, 4 (02) :223-295

[8] FINITE-ENERGY SOLUTIONS OF THE YANG-MILLS EQUATIONS IN R(3+1) [J].

KLAINERMAN, S ;

MACHEDON, M .

ANNALS OF MATHEMATICS, 1995, 142 (01) :39-119

[9] On the optimal local regularity for the Yang-Mills equations in R4+1 [J].

Klainerman, S ;

Tataru, D .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 12 (01) :93-116

[10] Global well-posedness for the Yang-Mills equation in 4+1 dimensions. Small energy [J].

Krieger, Joachim ;

Tataru, Daniel .

ANNALS OF MATHEMATICS, 2017, 185 (03) :831-893

← 1 2 →