Electron. J. Diff. Equ., Vol. 2015 (2015), No. 299, pp. 1-14.

Global solutions for 2D coupled Burgers-complex-Ginzburg-Landau equations

Hongjun Gao, Lin Lin, Yajun Chu

Abstract:
In this article, we study the periodic initial-value problem of the 2D coupled Burgers-complex-Ginzburg-Landau (Burgers-CGL) equations. Applying the Brezis-Gallout inequality which is available in 2D case and establishing some prior estimates, we obtain the existence and uniqueness of a global solution under certain conditions.

Submitted June 2, 2015. Published December 7, 2015.
Math Subject Classifications: 35M13, 35D35.
Key Words: Burgers-CGL equation; prior estimate; global solution; Gagliardo-Nirenberg inequality; Holder inequality.

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  Hongjun Gao
Institute of Mathematics
School of Mathematical Sciences
Nanjing Normal University
Nanjing 210023, China
email: gaohj@njnu.edu.cn
Lin Lin (corresponding author)
Institute of Mathematics
School of Mathematical Sciences
Nanjing Normal University
Nanjing 210023, China
email: linlin@njnu.edu.cn
  Yajun Chu
Institute of Mathematics
School of Mathematical Sciences
Nanjing Normal University
Nanjing 210023, China
email: chuyjnjnu@163.com

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