Geodesic
The Rothe method and time periodic solutions to the Navier-Stokes equations and equations of magnetohydrodynamics
Applications of Mathematics, Tome 35 (1990) no. 2, pp. 89-98.

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The existence of a periodic solution of a nonlinear equation $z' + A_0z + B_0z=F$ is proved. The theory developed may be used to prove the existence of a periodic solution of the variational formulation of the Navier-Stokes equations or the equations of magnetohydrodynamics. The proof of the main existence theorem is based on Rothe method in combination with the Galerkin method, using the Brouwer fixed point theorem.
DOI : 10.21136/AM.1990.104392
Classification : 35A15, 35Q10, 35Q30, 65J15, 65M20, 65N40, 76D05, 76M10
Keywords: Navier-Stokes equations; periodic solutions; existence of generalized solutions; nonlinear operator equation; variational formulation; equations of magnetohydrodynamics; Galerkin method; Brouwer fixed point theorem 
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     title = {The {Rothe} method and time periodic solutions to the {Navier-Stokes} equations and equations of magnetohydrodynamics},
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Lauerová, Dana. The Rothe method and time periodic solutions to the Navier-Stokes equations and equations of magnetohydrodynamics. Applications of Mathematics, Tome 35 (1990) no. 2, pp. 89-98. doi : 10.21136/AM.1990.104392. http://geodesic.mathdoc.fr/articles/10.21136/AM.1990.104392/

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