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arXiv · 1504.00808

Stable blowup for wave equations in odd space dimensions

Roland Donninger·Birgit Schörkhuber
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Abstract

We consider semilinear wave equations with focusing power nonlinearities in odd space dimensions $d \geq 5$. We prove that for every $p > \frac{d+3}{d-1}$ there exists an open set of radial initial data in $H^{\frac{d+1}{2}} \times H^{\frac{d-1}{2}}$ such that the corresponding solution exists in a backward lightcone and approaches the ODE blowup profile. The result covers the entire range of energy supercritical nonlinearities and extends our previous work for the three-dimensional radial wave equation to higher space dimensions.

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Roland Donninger, Birgit Schörkhuber. 2015-04-03. Stable blowup for wave equations in odd space dimensions. https://arxiv.org/abs/1504.00808

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