Local well-posedness and parabolic smoothing of solutions of fully nonlinear third-order equations on the torus

Tristan Roy

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arXiv · 2102.02689

Local well-posedness and parabolic smoothing of solutions of fully nonlinear third-order equations on the torus

Tristan Roy

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Abstract

We study the initial value problem of fully nonlinear third-order equations on the torus. Under some conditions on the nonlinearity and the data, we prove that the equation behaves like a parabolic one: there exists a unique local solution in one direction of time that is infinitely smooth and the problem in not well-posed in the other direction. Under other conditions on the nonlinearity and the data, we prove that the equation behaves like a dispersive one: there exists a unique local solution in both directions of time.

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Tristan Roy. 2021-02-04. Local well-posedness and parabolic smoothing of solutions of fully nonlinear third-order equations on the torus. https://arxiv.org/abs/2102.02689

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