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On the Stability of the Notion of Non-Characteristic Point and Blow-Up Profile for Semilinear Wave Equations

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Abstract

We consider a blow-up solution for the semilinear wave equation in N dimensions, with subconformal power nonlinearity. Introducing \({\mathcal{R}_0}\) the set of non-characteristic points with the Lorentz transform of the space-independent solution as asymptotic profile, we show that \({\mathcal{R}_0}\) is open and that the blow-up surface is of class C 1 on \({\mathcal{R}_0}\) . Then, we show the stability of \({\mathcal{R}_0}\) with respect to initial data.

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Authors and Affiliations

  1. Département de mathématiques, Université de Cergy Pontoise and IHES, 2 avenue Adolphe Chauvin, BP 222, 95302, Cergy Pontoise cedex, France

    Frank Merle

  2. Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), 93430, Villetaneuse, France

    Hatem Zaag

Authors
  1. Frank Merle
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  2. Hatem Zaag
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Correspondence to Hatem Zaag.

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Communicated by W. Schlag

Both authors are supported by the ERC Advanced Grant no. 291214, BLOWDISOL. H.Z. is partially supported by ANR project ANAÉ ref. ANR-13-BS01-0010-03.

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Merle, F., Zaag, H. On the Stability of the Notion of Non-Characteristic Point and Blow-Up Profile for Semilinear Wave Equations. Commun. Math. Phys. 333, 1529–1562 (2015). https://doi.org/10.1007/s00220-014-2132-8

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  • DOI: https://doi.org/10.1007/s00220-014-2132-8

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