Wednesday, June 17, 2020 - 15:00 in ZOOM - Video Conference
On the well-posedness of the complex-valued modified KdV equation on the circle outside of $H^{(1/2)}$
A talk in the Oberseminar Analysis series by
Andreia Chapouto from The University of Edinburgh
| Abstract: |
Meeting ID: 951 9741 9687 Password: 82787
In this talk, we consider the low regularity well-posedness of the complex-valued modified Korteweg-de Vries equation (mKdV) with periodic initial data. Although in the real-valued setting it suffices to renormalize the equation based on the conservation of mass, for complex-valued mKdV the conservation of momentum also plays an important role. In particular, we show that mKdV is ill-posed in the sense of non-existence of solution for initial data with infinite momentum. Consequently, we introduce a further renormalization based on the momentum and show well-posedness of the new equation in certain Fourier-Lebesgue spaces, using the method introduced by Deng-Nahmod-Yue. Lastly, by imposing a new notion of 'finite' momentum, we relate our low regularity well-posedness results back to the original mKdV equation.
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