The Lagrange multiplier and the stationary Stokes equations
-
Wojciech S. Ożański
Abstract
We briefly discuss the notion of the Lagrange multiplier for a linear constraint in the Hilbert space setting, and we prove that the pressure p appearing in the stationary Stokes equations is the Lagrange multiplier of the constraint
Funding source: Engineering and Physical Sciences Research Council
Award Identifier / Grant number: EP/HO23364/1
Funding statement: The author is supported by EPSRC as part of the MASDOC DTC at the University of Warwick, Grant No. EP/HO23364/1.
References
[1] C. M. Elliott, Optimisation and fixed point theory, Lecture notes, University of Warwick, 2014. Search in Google Scholar
[2] V. Girault and P.-A. Raviart, Finite Element Methods for Navier–Stokes Equations, Springer Ser. Comput. Math. 5, Springer, Berlin, 1986. 10.1007/978-3-642-61623-5Search in Google Scholar
[3] R. Temam, Navier–Stokes Equations, Theory and Numerical Analysis. Reprint of the 1984 Edition, American Mathematical Society, Providence, 2001. 10.1090/chel/343Search in Google Scholar
[4] K. Yosida, Functional Analysis. Reprint of the Sixth (1980) Edition, Classics Math., Springer, Berlin, 1995. 10.1007/978-3-642-61859-8Search in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Dynamics of typical Baire-1 functions on the interval
- On the generalized quotient integrals on homogeneous spaces
- An integral expression for the Dunkl kernel in the dihedral setting
- Takagi function revisited
- On the stability of steady-states of a two-dimensional system of ferromagnetic nanowires
- Pexider type equation on a region
- Anti-periodic solutions for a higher order difference equation with p-Laplacian
- Portfolio immunization under cone restrictions
- The Lagrange multiplier and the stationary Stokes equations
- Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument
Articles in the same Issue
- Frontmatter
- Dynamics of typical Baire-1 functions on the interval
- On the generalized quotient integrals on homogeneous spaces
- An integral expression for the Dunkl kernel in the dihedral setting
- Takagi function revisited
- On the stability of steady-states of a two-dimensional system of ferromagnetic nanowires
- Pexider type equation on a region
- Anti-periodic solutions for a higher order difference equation with p-Laplacian
- Portfolio immunization under cone restrictions
- The Lagrange multiplier and the stationary Stokes equations
- Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument
