New Results on Gevrey Well Posedness for the Schrödinger–Korteweg–De Vries System
Abstract
:1. Introduction
2. Notations and Function Spaces
3. Auxiliary Estimates
- (1)
- ;
- (2)
- ;
- (3)
- 1/
- for ;
- 2/
- for and .
- (i)
- ;
- (ii)
- .
4. Local Well Posedness and Proof
5. Regularity of Solution
6. Conclusions
- Developing estimates for the cubic nonlinear terms (9) and (10);
- Establishing bilinear estimates for the interaction terms presented in (16) and (17);
- Enhancing the proof of solution regularity by refining the estimates (34) and (35).
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Boudersa, F.; Mennouni, A.; Agarwal, R.P. New Results on Gevrey Well Posedness for the Schrödinger–Korteweg–De Vries System. Math. Comput. Appl. 2025, 30, 52. https://doi.org/10.3390/mca30030052
Boudersa F, Mennouni A, Agarwal RP. New Results on Gevrey Well Posedness for the Schrödinger–Korteweg–De Vries System. Mathematical and Computational Applications. 2025; 30(3):52. https://doi.org/10.3390/mca30030052
Chicago/Turabian StyleBoudersa, Feriel, Abdelaziz Mennouni, and Ravi P. Agarwal. 2025. "New Results on Gevrey Well Posedness for the Schrödinger–Korteweg–De Vries System" Mathematical and Computational Applications 30, no. 3: 52. https://doi.org/10.3390/mca30030052
APA StyleBoudersa, F., Mennouni, A., & Agarwal, R. P. (2025). New Results on Gevrey Well Posedness for the Schrödinger–Korteweg–De Vries System. Mathematical and Computational Applications, 30(3), 52. https://doi.org/10.3390/mca30030052