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arXiv · 1510.02730

Determining form and data assimilation algorithm for weakly damped and driven Korteweg-de Vries equaton- Fourier modes case

Michael S. Jolly·Tural Sadigov·Edriss S. Titi
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Abstract

We show that the global attractor of a weakly damped and driven Korteweg-de Vries equation (KdV) is embedded in the long-time dynamics of an ordinary differential equation called a determining form. In particular, there is a one-to-one identification of the trajectories in the global attractor of the damped and driven KdV and the steady state solutions of the determining form. Moreover, we analyze a data assimilation algorithm (down-scaling) for the weakly damped and driven KdV. We show that given a certain number of low Fourier modes of a reference solution of the KdV equation, the algorithm recovers the full reference solution at an exponential rate in time.

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Michael S. Jolly, Tural Sadigov, Edriss S. Titi. 2015-10-09. Determining form and data assimilation algorithm for weakly damped and driven Korteweg-de Vries equaton- Fourier modes case. https://arxiv.org/abs/1510.02730

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