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Regularity of Solutions to the Navier-Stokes Equations with a Nonstandard Boundary Condition

Regularity of Solutions to the Navier-Stokes Equations with a Nonstandard Boundary Condition
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摘要 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. 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.
作者 Tujin KIM
机构地区 Institute of Mathematics
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2015年第3期707-718,共12页 应用数学学报（英文版）
基金 Supported by TWAS,UNESCO and AMSS in Chinese Academy of Sciences
关键词 Navier-Stokes equation regularity boundary condition on the pressure Navier-Stokes equation regularity boundary condition on the pressure
分类号 O175 [理学—基础数学]
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参考文献15

  • 1Amara, M., Vera, E.C., Tpujillo, D. A three field stabilized finite element method for the Stokes equations. C.R. Acad. Sci. Paris, Serie I, 334:603-608 (2002).
  • 2Alekseev, G.V., Smishliaev, A.B. Solvability of the boundary value problems for Boussinesq equations with inhomogeneous boundary conditions. J. Math. Fluid Mech., 3:18- 39 (2001).
  • 3Begue, C., Conca, C., Murat, F., Pironneau, O. A nouveau sur les equations de Stokes et de Navier-Stokes avec des conditions aux limites sur la pression. C.R. Acad. Sci. Paris, Seriei, 304:23 -28 (1987).
  • 4Begue, C., Conca, C., Murat, F., Pironneau, O. Les equations de Stokes et de Navier-Stokes avec des condition sur la pression. Nonlinear Partial Differential Equations and Their Applications, College de France, Seminar, Vol. Ⅸ, 179-384, Pitman Advanced Publishing Program, Boston, London, Melbourne, 1988.
  • 5Bernard, J.M. Non-standard Stokes and Navier-Stokes problems: existence and regularity in stationary case. Mathematical Methods in the Applied Sciences, 25:627-661 (2002).
  • 6Bernard, J.M. Time-dependent Stokes and Navier-Stokes problems with boundary conditions involving pressure:existence and regularity. Nonlinear Analysis: Real World Application, 4:805-839 (2003).
  • 7Bergh, J., L6fstr6m, J. Interpolation Spaces, Springer-Verlag, Berlin, Heidelberg, New York, 1976.
  • 8Ciarlet, P. System de Stokes avec flux de vitesse et pression imposes. C.R. Acad. Sci. Paris, Serie I. 337: 119-124 (2003).
  • 9Conca, C., Murat, F., Pironneau, O. The Stokes and Navier-Stokes equations with boundary conditions involving the pressure. Japan. J. Math., 20 2:279-318 (1994).
  • 10Conca, C., Pares, C., Pironneau, O., Thiriet, M. Navier-Stokes equations with imposed pressure and velocity fluxes. International J. for Numerical Methods in Fluid, 20:267-287 (1995).
Acta Mathematicae Applicatae Sinica
2015年 第3期

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