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- W2897618054 abstract "Inertial manifolds of Navier-Stokes equations have been calculated approximately up to now. In thispaper, drawing upon advanced ingredients of differential geometry and Lie groups a novel methodology ispresented for finding the inertial manifolds of ( ) +12 -dimensional Navier-Stokes equation. It has been shownthat the geometric notions about Lie groups and Lie algebras such as transformation groups, one-parametergroups, integral submanifolds, adjoint representations, group-invariant solutions and optimal systems not onlycover all of the properties of inertial manifolds, but also result to the exact decomposition of the velocity fieldof the flow of Navier-Stokes equation by proposing the coordinate chart for it. In this way, the new procedureoutperforms the numerical estimation methods by providing the analytic solution of the inertial manifolds.Also, the proposed methodology can be applied to the general problems by searching the optimal systems ofthem. Furthermore, this geometric approach results to the reduction theory which transforms these partialdifferential equations into a system of differential equations with fewer variables." @default.
- W2897618054 created "2018-10-26" @default.
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- W2897618054 date "2018-01-01" @default.
- W2897618054 modified "2023-09-24" @default.
- W2897618054 title "Inertial Manifolds for Navier-Stokes Equations in Notions of Lie Algebras" @default.
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