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arXiv · 1504.01136

Global existence of radial solutions for general semilinear hyperbolic systems in 3D

Silu Yin·Yi Zhou
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Abstract

We study the well-posedness of radial solutions for general nonlinear hyperbolic systems in three dimensions. We give a proof of the global existence of radial solutions for general semilinear hyperbolic systems in 3D under null condition, with small scaling invariant $\dot{W}^{2,1}(\mathbb{R}^3)$ data. We obtain a bilinear estimate that is effective to the hyperbolic systems which do not have any time decay. It allows us to achieve the boundedness of the weighted BV norm of the radial solution.

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Silu Yin, Yi Zhou. 2015-04-05. Global existence of radial solutions for general semilinear hyperbolic systems in 3D. https://arxiv.org/abs/1504.01136

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