http://arxiv.org/abs/1709.03356
To understand and model non-ideal flows, we use the simple result $(\partial_t + L_v) (\omega_1 \wedge \omega_2) = S_1 \wedge \omega_2 + \omega_1 \wedge S_2$ from the Lie-varying forms $(\partial_t + L_v) \omega_i = S_i: \ i = 1, 2$. If the (Lie-)sources/sinks satisfy $S_1 \wedge \omega_2 + \omega_1 \wedge S_2 = 0$, a
multiplicative' Lie invariant follows, extending the classical approaches offinding new invariants from known ones of ideal flows’ and of modeling non-ideal flows constrained by invariant(s), beyond the traditional ones, the Gauss method, say. Precise relations, such as the generalised Cauchy invariants equation, as found here for two-fluid plasma dynamics, also extend to wider application space.
J. Zhu
Tue, 12 Sep 17
65/71
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