A completely KdV-type Boussinesq system in low regularity spaces

• Autores: Montealegre, Juan, Pérez, Zelideth
• Formato: artículo
• Fecha de Publicación: 2018
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/1972
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/1972
• Nivel de acceso: acceso abierto
• Materia: Cauchy problem; Korteweg-de Vries equations; Global well posedness; Bourgain spaces; almost conservation laws; Problema de Cauchy; Ecuación de Korteweg-de Vries; Buena formulación global; Espacios de Bourgain; cantidades casi conservadas

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-posednessin 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].