THE CAUCHY PROBLEM OF A PERIODIC KAWAHARA EQUATION IN ANALYTIC GEVREY SPACES

Aissa BOUKAROU; Kaddour GUERBATİ

doi:https://doi.org/10.47087/mjm.930045

Article Details

THE CAUCHY PROBLEM OF A PERIODIC KAWAHARA EQUATION IN ANALYTIC GEVREY SPACES

Authors:

Aissa BOUKAROU | Kaddour GUERBATİ

Publisher:

Hüseyin ÇAKALLI

Main Topics:

Mathematics

Journal:

Maltepe Journal of Mathematics 2021 Vol.3 Issue 2, pp.91-100

Document Type:

Article

Publication Date:

10/2021

Document Language:

English

Document ID (Org No.):

2000526645

Frequency:

Bi-Annual

pISSN:

2667-7660

DOI:

https://doi.org/10.47087/mjm.930045

Abstract:

 

The Cauchy problem for the Kawahara equation with data in analytic Gevrey spaces on the circle is considered and its local well-posedness in these spaces is proved. Using Bourgain-Gevrey type analytic spaces and appropriate bilinear estimates, it is shown that local in time wellposedness holds when the initial data belong to an analytic Gevrey spaces of order σ. Moreover, the solution is not necessarily Gσ in time. However, it belongs to G5σ near zero for every x on the circle. We study a Cauchy problem for Kawahara equation . With data in analytic Gevrey spaces on the circal, we prove that the problem is well defined. We also treat the regularity  in time which belongs to G5σG5σG^{5\sigma} .

Article Details

THE CAUCHY PROBLEM OF A PERIODIC KAWAHARA EQUATION IN ANALYTIC GEVREY SPACES

Authors: Aissa BOUKAROU | Kaddour GUERBATİ

Publisher: Hüseyin ÇAKALLI

Main Topics: Mathematics

Journal: Maltepe Journal of Mathematics 2021 Vol.3 Issue 2, pp.91-100

Document Type: Article

Publication Date: 10/2021

Document Language: English

Document ID (Org No.): 2000526645

Frequency: Bi-Annual

pISSN: 2667-7660

DOI: https://doi.org/10.47087/mjm.930045

Issues

Authors:

Aissa BOUKAROU | Kaddour GUERBATİ

Publisher:

Hüseyin ÇAKALLI

Main Topics:

Mathematics

Journal:

Maltepe Journal of Mathematics 2021 Vol.3 Issue 2, pp.91-100

Document Type:

Article

Publication Date:

10/2021

Document Language:

English

Document ID (Org No.):

2000526645

Frequency:

Bi-Annual

pISSN:

2667-7660

DOI:

https://doi.org/10.47087/mjm.930045