Well posedness and stability in the periodic case for the Benney system

Angulo J., Corcho A., HAKKAEV S. A.

Advances in Differential Equations, cilt.16, sa.5-6, ss.523-550, 2011 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 5-6
  • Basım Tarihi: 2011
  • Dergi Adı: Advances in Differential Equations
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.523-550
  • Trakya Üniversitesi Adresli: Hayır

Özet

We establish local well-posedness results in weak periodic function spaces for the Cauchy problem of the Benney system. The Sobolev space H1/2×L2 is the lowest regularity attained and also we cover the energy space H1×L2, where global well posedness follows from the conservation laws of the system. Moreover, we show the existence of a smooth explicit family of periodic travelling waves of dnoidal type and we prove, under certain conditions, that this family is orbitally stable in the energy space.