| Abstract: |
| This talk focuses on the well-posedness of the derivative nonlinear Schr\odinger equation on the line. This model is known to be completely integrable and $L^2$-critical with respect to scaling. However, until recently not much was known regarding the well-posendess of the equation below $H^{\frac 1 2}$. In this talk we prove that the problem is well-posed in the critical space $L^2$ on the line, highlighting several recent results that led to this resolution. This is joint work with Benjamin Harrop-Griffiths, Rowan Killip, and Monica Visan. |
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