Well-Posedness For The Dispersive Hunter-Saxton Equation

The HADES seminar on Tuesday, October 12th, will be given by Ovidiu-Neculai Avadanei at 5 pm in 740 Evans.

Speaker: Ovidiu-Neculai Avadanei

Abstract: This talk represents a first step towards understanding the well-posedness for the dispersive Hunter-Saxton equation. This problem arises in the study of nematic liquid crystals, and its non-dispersive version is known to be completely integrable. Although the equation has formal similarities with the KdV equation, the lack of $L^2$ control gives it a quasilinear character, with only continuous dependence on initial data. Here, we prove the local and global well-posedness of the Cauchy problem using a normal form approach to construct modified energies, and frequency envelopes in order to prove the continuous dependence with respect to the initial data. This is joint work with Albert Ai.

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