Regularity of solutions to the Navier-Stokes equations with a nonstandard boundary condition

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• 作者：Tujin Kim
• 关键词：Navier ; Stokes equation ; regularity ; boundary condition on the pressure ; 35Q30 ; 76D05 ; 76D07 ; 76N10
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：31
• 期：3
• 页码：707-718
• 全文大小：254 KB
• 参考文献：[1]Amara, M., Vera, E.C., Tpujillo, D. A three field stabilized finite element method for the Stokes equations. C.R. Acad. Sci. Paris, Serie I, 334: 603-08 (2002)View Article
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  [10]Conca, C., Pares, C., Pironneau, O., Thiriet, M. Navier-Stokes equations with imposed pressure and velocity fluxes. International J. for Numerical Methods in Fluid, 20: 267-87 (1995)MathSciNet View Article
  [11]Galdi, G.P. An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I, Springer-Verlag, New York, 1994
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• 作者单位：Tujin Kim (1)
  
  1. Institute of Mathematics, Academy of Sciences, Pyonyang, DPR Korea
  
• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932

文摘

In this paper we are concerned with the regularity of solutions to the Navier-Stokes equations with the condition on the pressure on parts of the boundary where there is flow. For the steady Stokes problem a result similar to L q -theory for the one with Dirichlet boundary condition is obtained. Using the result, for the steady Navier-Stokes equations we obtain regularity as the case of Dirichlet boundary conditions. Furthermore, for the time-dependent 2-D Navier-Stokes equations we prove uniqueness and existence of regular solutions, which is similar to J.M.Bernard’s results[6] for the time-dependent 2-D Stokes equations.