ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER-STOKES EQUATIONS

数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (3): 342-351.

ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER-STOKES EQUATIONS

唐贤江

Dept. of Math., Sichuan university, Chengdu 610064, China

收稿日期:1993-02-17 修回日期:1994-04-05 出版日期:1995-09-25 发布日期:1995-09-25

ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER-STOKES EQUATIONS

Tang Xianjiang

Dept. of Math., Sichuan university, Chengdu 610064, China

Received:1993-02-17 Revised:1994-04-05 Online:1995-09-25 Published:1995-09-25

摘要/Abstract

摘要： In this paper we discuss the mixed boundary problem (1)-(3) of the Navier-Stokes equations for the flow of an incompressible viscous fluid in a bounded domain. We prove that when g∈L^∞(Q),φ∈C¹(Γ₁×[0,t₁]),and ψ∈L¹(Γ₂×[0,t₁]),there exists a weak solution of (1)-(3),and when u∈L²(0,t₁;H³(Ω)),T∈L²(0,t₁;H³(Ω)),the weak solution is unique,if it exists.

关键词: Navier-Stokes equations, weak solution, mixed boundary poblem

Abstract: In this paper we discuss the mixed boundary problem (1)-(3) of the Navier-Stokes equations for the flow of an incompressible viscous fluid in a bounded domain. We prove that when g∈L^∞(Q),φ∈C¹(Γ₁×[0,t₁]),and ψ∈L¹(Γ₂×[0,t₁]),there exists a weak solution of (1)-(3),and when u∈L²(0,t₁;H³(Ω)),T∈L²(0,t₁;H³(Ω)),the weak solution is unique,if it exists.

Key words: Navier-Stokes equations, weak solution, mixed boundary poblem

唐贤江. ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER-STOKES EQUATIONS[J]. 数学物理学报(英文版), 1995, 15(3): 342-351.

Tang Xianjiang. ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER-STOKES EQUATIONS[J]. Acta mathematica scientia,Series B, 1995, 15(3): 342-351.

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ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER-STOKES EQUATIONS

ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER-STOKES EQUATIONS

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