Abstract
In this paper we analyze the stronger singularities of solutions \( u \in H_{\text{loc}}^s(\Omega ),s < \frac{n}{2} \), for semilinear wave equations, using the microlocal multiplication of the solutions, the fact of the loss in smoothness of the products in H s, s < n/2, and the trick of reducing the loss in smoothness of the products.
Résumé
Dans cet article, nous analysons les plus fortes singularités des solutions u ∈ \( u \in H_{\text{loc}}^s(\Omega ),s < \frac{n}{2} \), s < n/2, des équations d’ondes semi-linéaires en utilisant la multiplication microlocale des solutions, le fait de la perte de lissage du produit dans H s, s < n/2, et le truc de réduire la perte de lissage du produit.
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© 1991 Springer-Verlag New York, Inc.
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Linqi, L. (1991). Propagation of Stronger Singularities of Solutions to Semilinear Wave Equations. In: Beals, M., Melrose, R.B., Rauch, J. (eds) Microlocal Analysis and Nonlinear Waves. The IMA Volumes in Mathematics and its Applications, vol 30. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9136-4_10
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DOI: https://doi.org/10.1007/978-1-4613-9136-4_10
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