Well-Posedness and Time Regularity for a System of Modified Korteweg-de Vries-Type Equations in Analytic Gevrey Spaces

Aissa Boukarou, Kaddour Guerbati, Khaled Zennir, Sultan Alodhaibi and Salem Alkhalaf
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Aissa Boukarou: Laboratoire de Mathématiques et Sciences Appliquées, Université de Ghardaia, Ghardaia 47000, Algerie
Kaddour Guerbati: Laboratoire de Mathématiques et Sciences Appliquées, Université de Ghardaia, Ghardaia 47000, Algerie
Khaled Zennir: Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia
Sultan Alodhaibi: Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia
Salem Alkhalaf: Computer Department, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia

Mathematics, 2020, vol. 8, issue 5, 1-16

Abstract: Studies of modified Korteweg-de Vries-type equations are of considerable mathematical interest due to the importance of their applications in various branches of mechanics and physics. In this article, using trilinear estimate in Bourgain spaces, we show the local well-posedness of the initial value problem associated with a coupled system consisting of modified Korteweg-de Vries equations for given data. Furthermore, we prove that the unique solution belongs to Gevrey space G σ × G σ in x and G 3 σ × G 3 σ in t . This article is a continuation of recent studies reflected.

Keywords: modified Korteweg-de Vries equations; well-posedness; analytic Gevrey spaces; Bourgain spaces; trilinear estimates; time regularity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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