A time periodic solution of the Navier-Stokes equations with mixed boundary conditions
Kučera, Petr
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Kučera, Petr
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Hu, Xianpeng (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Saks, R.S. (2004)
Zapiski Nauchnykh Seminarov POMI
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Dana Lauerová (1990)
Aplikace matematiky
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The existence of a periodic solution of a nonlinear equation 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.
Saut, J.C. (1982)
Portugaliae mathematica
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Giovanni Prouse (1992)
Banach Center Publications
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A Navier-Stokes type equation corresponding to a non-linear relationship between the stress tensor and the velocity deformation tensor is studied and existence and uniqueness theorems for the solution, in the 3-dimensional case, of the Cauchy-Dirichlet problem, for a bounded solution and for an almost periodic solution are given. An inequality which in some sense is the limit of the equation is also considered and existence theorems for the solution of the Cauchy-Dirichlet problems and...