Fabrice Planchon (1998)
Revista Matemática Iberoamericana
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We construct global solutions to the Navier-Stokes equations with initial data small in a Besov space. Under additional assumptions, we show that they behave asymptotically like self-similar solutions.
F. Benatti (1993)
Annales de l'I.H.P. Physique théorique
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Eugène Gutkin (1986)
Annales de l'I.H.P. Analyse non linéaire
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Cardoso, Fernando, Cuevas, Claudio, Vodev, Georgi (2005)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 35L15, 35B40, 47F05. We prove dispersive estimates for solutions to the wave equation with a real-valued potential V.
Catherine Bolley, Bernard Helffer (1997)
Annales de l'I.H.P. Analyse non linéaire
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Amel Atallah Baraket (2004)
Bollettino dell'Unione Matematica Italiana
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In this paper we prove a local existence theorem for a Cauchy problem associated to a semi linear wave equation with an exponential nonlinearity in two dimension space. In this problem, the first Cauchy data is equal to zero, the second is in , radially symmetric and compactly supported. To prove this theorem, we first show a Moser-Trudinger type inequality for the linear problem and then we use a fixed point method to achieve the proof of the result.