A completely KdV-type Boussinesq system in low regularity spaces

Authors

  • Juan Montealegre Pontificia Universidad Católica del Perú, Departamento de Ciencias. Av. Universitaria 1801, San Miguel, Lima 32, Perú.
  • Zelideth Pérez Universidad Nacional Agraria La Molina, Facultad de Ciencias. Av. La Molina s/n, La Molina, Lima 12, Perú.

DOI:

https://doi.org/10.17268/sel.mat.2018.01.03

Keywords:

Cauchy problem, Korteweg-de Vries equations, Global well posedness, Bourgain spaces, almost conservation laws

Abstract

In this paper we study the well-posedness of Cauchy problem for a Boussinesq system formed by two Kortewegde Vries equations coupled through the linear part and the non-linear terms. First we proof its local well-posedness
in the Sobolev spaces Hs (R) x Hs (R), s > -3/4, using the bilinear estimate established by Kenig, Ponce and Vega in the Fourier transform restriction spaces [4, 12]. After, we prove the global well-posedness in Hs (R) x Hs (R) for s > -3/10, our proof proceeds by the method of almost conservation laws, sometimes called the “I-method”[5, 6].

References

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Published

2018-07-27

How to Cite

Montealegre, J., & Pérez, Z. (2018). A completely KdV-type Boussinesq system in low regularity spaces. Selecciones Matemáticas, 5(01), 17 - 26. https://doi.org/10.17268/sel.mat.2018.01.03

Issue

Vol. 5 No. 01 (2018): January - July

Section

Articles

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