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Optimal blowup stability for three-dimensional wave maps

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arxiv 2212.08374 v3 pith:V6WX7B33 submitted 2022-12-16 math.AP math-phmath.MP

Roland Donninger , David Wallauch This is my paper
classification math.APmath-phmath.MP
keywords wavespacecriticalmapssobolevstabilityaccomplishedasymptotic
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abstract

We study corotational wave maps from $(1+3)$-dimensional Minkowski space into the three-sphere. We establish the asymptotic stability of an explicitly known self-similar wave map under perturbations that are small in the critical Sobolev space. This is accomplished by proving Strichartz estimates for a radial wave equation with a potential in similarity coordinates. Compared to earlier work, the main novelty lies with the fact that the critical Sobolev space is of fractional order.

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