ON THE CAUCHY PROBLEM OF THE KURAMOTO-SIVASHINSKY EQUATION WITH SINGULAR INITIAL DATA

数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (1): 25-34.

ON THE CAUCHY PROBLEM OF THE KURAMOTO-SIVASHINSKY EQUATION WITH SINGULAR INITIAL DATA

赵会江¹, 柳再华², 陈世平³

1. Young Scientist Laboratory of Mathematical Physics, Wnhan Institute of Physics and Mathematics Academia Sinica, Wuhan 430071, China;
2. Tongji University of Medicine, Wuhan 430040, China;
3. Zhuzhou Institute, of Techonology, Zhuzhou 412008, China

收稿日期:1995-09-22 修回日期:1996-03-09 出版日期:1998-03-25 发布日期:1998-03-25
基金资助:
This work is partially supported by Youth Foundation NNSFC

ON THE CAUCHY PROBLEM OF THE KURAMOTO-SIVASHINSKY EQUATION WITH SINGULAR INITIAL DATA

Zhao Huijiang¹, Liu Zaihua², Chen Shiping³

1. Young Scientist Laboratory of Mathematical Physics, Wnhan Institute of Physics and Mathematics Academia Sinica, Wuhan 430071, China;
2. Tongji University of Medicine, Wuhan 430040, China;
3. Zhuzhou Institute, of Techonology, Zhuzhou 412008, China

Received:1995-09-22 Revised:1996-03-09 Online:1998-03-25 Published:1998-03-25
Supported by:
This work is partially supported by Youth Foundation NNSFC

摘要/Abstract

摘要： In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Stvashinsky equation
u_t+1/2▽(|u|²)+△u+△²u=0,t>0,x∈R^N, u(0,x)=u₀(x),x∈R^N.
only under the condition u₀(x) ∈L²(R^N, Rⁿ). Where u(t, x)=(u₁ (t, x),…,u_n (t, x))^T is the unknown vector-valued function. Results show that for N < 6,u₀ (x) ∈L² (R^N, Rⁿ), the above Cauchy problem admits a unique global solution u(t, z) which belongs to C^∞,∞ (R^N×(0, ∞)).

关键词: Kuramoto-Sivashinsky equation, Singular initial data, Sobolev imbedding theorem

Abstract: In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Stvashinsky equation
u_t+1/2▽(|u|²)+△u+△²u=0,t>0,x∈R^N, u(0,x)=u₀(x),x∈R^N.
only under the condition u₀(x) ∈L²(R^N, Rⁿ). Where u(t, x)=(u₁ (t, x),…,u_n (t, x))^T is the unknown vector-valued function. Results show that for N < 6,u₀ (x) ∈L² (R^N, Rⁿ), the above Cauchy problem admits a unique global solution u(t, z) which belongs to C^∞,∞ (R^N×(0, ∞)).

Key words: Kuramoto-Sivashinsky equation, Singular initial data, Sobolev imbedding theorem

赵会江, 柳再华, 陈世平. ON THE CAUCHY PROBLEM OF THE KURAMOTO-SIVASHINSKY EQUATION WITH SINGULAR INITIAL DATA[J]. 数学物理学报(英文版), 1998, 18(1): 25-34.

Zhao Huijiang, Liu Zaihua, Chen Shiping. ON THE CAUCHY PROBLEM OF THE KURAMOTO-SIVASHINSKY EQUATION WITH SINGULAR INITIAL DATA[J]. Acta mathematica scientia,Series B, 1998, 18(1): 25-34.

ON THE CAUCHY PROBLEM OF THE KURAMOTO-SIVASHINSKY EQUATION WITH SINGULAR INITIAL DATA

ON THE CAUCHY PROBLEM OF THE KURAMOTO-SIVASHINSKY EQUATION WITH SINGULAR INITIAL DATA

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