| Abstract: |
| We show the orbital stability of solitons arising in the cubic derivative nonlinear Schr\"odinger equations. We consider the endpoint case the the gauge transform has zero mass. As opposed to other cases, this case enjoys $L^2$ scaling invariance. So we expect the orbital stability in the sense up to scaling symmetry, in addition to spatial and phase translations. FOr the proof, we are based on the variational argument and extend a similar argument that was used for the proof of global existence for solutions with mass less than $4 \pi$. Moreover, we also show a self-similar type blow up criteria with critical mass $4\pi$. This is a joint work with Yifei Wu. |
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