scholarly journals Global Well-Posedness for Dissipative Korteweg-de Vries Equations

2011 ◽  
Vol 54 (1) ◽  
pp. 119-138 ◽  
Author(s):  
Stéphane Vento
Keyword(s):  
Well Posedness ◽  
De Vries

scholarly journals On unconditional well-posedness for the periodic modified Korteweg–de Vries equation

2019 ◽  
Vol 71 (1) ◽  
pp. 147-201 ◽  
Author(s):  
Luc MOLINET ◽  
Didier PILOD ◽  
Stéphane VENTO
Keyword(s):  
Vries Equation ◽  
Well Posedness ◽  
De Vries

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

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 809
Author(s):  
Aissa Boukarou ◽  
Kaddour Guerbati ◽  
Khaled Zennir ◽  
Sultan Alodhaibi ◽  
Salem Alkhalaf
Keyword(s):  
Unique Solution ◽  
Initial Value Problem ◽  
Coupled System ◽  
Well Posedness ◽  
Initial Value ◽  
Gevrey Spaces ◽  
De Vries ◽  
Gevrey Space

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.

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