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arXiv · 2207.02076

The global solvability of the Kirchhoff equation with Sobolev data

Tokio Matsuyama·Lenny Neyt
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Abstract

We consider linear and non-linear Cauchy equations in the context of Sobolev spaces. In particular, we show the global existence of solutions to the Kirchhoff equation with initial data in the Sobolev spaces, a problem that has been open for more than eighty years. Our proof is based on a new uniform estimate for solutions to the linear equation with time-dependent coefficient and a fixed point argument. As an immediate consequence of our result, the global solvability of the Kirchhoff equation with initial data in the Gevrey spaces is also obtained.

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Tokio Matsuyama, Lenny Neyt. 2022-07-05. The global solvability of the Kirchhoff equation with Sobolev data. https://arxiv.org/abs/2207.02076

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