Two-speed DDNLW
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Two-speed DDNLW
- One can consider two-speed variants of DDNLW ([#two-speed see Overview]), when both F and G have the form G (U) DU DU.
- The Strichartz and energy estimates carry over without difficulty to this setting. The results obtained by X^{s,\theta} estimates change, however. The null forms are no longer as useful, however the estimates are usually more favourable because of the transversality of the two light cones. Of course, if F contains DuDu or G contains DvDv then one cannot do any better than the one-speed case.
- For d=2 one can obtain LWP for the near-optimal range s>3/2 when F does not contain DuDu and G does not contain DvDv [Tg-p].
- For d=1 one can obtain LWP for the near-optimal range s>1 when F does not contain DuDu and G does not contain DvDv [Tg-p].
- For d=3 one can obtain GWP for small compactly supported data for quasilinear equations with multiple speeds, as long as the nonlinearity has no explicit dependence on U [KeSmhSo-p3]
A special case of two-speed DDNLS arises in elasticity (more on this to be added in later).
