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Time-weighted
estimates in Lorentz spaces and self-similarity for wave
equations with singular potentials
Marcelo F. de Almeida and Lucas C. F. Ferreira |
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Vol. 10 (2017), No. 2, 423–438
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Abstract |
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We show time-weighted estimates in Lorentz spaces for the linear wave equation with singular potential. As a consequence, assuming radial symmetry on initial data and potentials, we obtain well-posedness of global solutions in critical weak- spaces for semilinear wave equations. In particular, we can consider the Hardy potential for small . Self-similar solutions are obtained for potentials and initial data with the right homogeneity. Our approach relies on performing estimates in the predual of weak-, i.e., the Lorentz space . |
Keywords
wave equations, singular potentials, self-similarity,
radial symmetry, Lorentz spaces
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Mathematical Subject Classification 2010
Primary: 35L05, 35L71, 35L15, 35A01, 35B06
Secondary: 35C06, 42B35
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Milestones
Received: 2 July 2016
Accepted: 12 November 2016
Published: 23 February 2017
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Authors |
| Marcelo F. de Almeida | |
| Departamento de Matemática Universidade Federal de Sergipe, CCET Av. Marechal Rondon, s/n 49100-000 Aracaju-SE Brazil |
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| Lucas C. F. Ferreira | |
| Departamento de Matemática Universidade Estadual de Campinas, IMECC Rua Sérgio Buarque de Holanda, 651 13083-859 Campinas-SP Brazil |
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