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The dynamics of
uids are often studied through the reduction of partial di erential
equations to systems with only a few degrees of freedom. Analysis of these low dimensional
vector elds remains ...
Two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations
Camassa–Holm equation Degasperis–Procesi equation semidirect product geodesic flow
2010/11/26
We use geometric methods to study two natural two-component generalizations of the periodic Camassa–Holm and Degasperis–Procesi equations.
Restrictions on the geometry of the periodic vorticity equation
Non-metric Euler equation geodesic flow diffeomor-phism group of the circle
2010/11/30
We prove that several evolution equations arising as mathematical models for fluid motion cannot be realized as metric Euler equations on the Lie group Diff1(S1) of all smooth and orientation-preservi...
Time-Periodic Solutions of the Einstein's Field Equations II: Geometric Singularities
Einstein's ˉeld equations time-periodic solution Riemann curvature tensor singu- larity event horizon
2018/4/20
In this paper, we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish, keep finite or take the infinity at some point...
In this paper, we prove the rules of direct addition and subtraction for the finite decimal expansions of fractions which are periodic. It has been shown that these rules are valid for the fractions w...