Well-posedness of the Cauchy problem and stability theory for nonlinear dispersive...
Decay estimates for hyperbolic partial differential equations in the L^p-L^q frame...
| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Fed Sao Carlos, Dept Math, BR-13565905 Sao Carlos, SP - Brazil
[2] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 - USA
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | JOURNAL OF EVOLUTION EQUATIONS; v. 21, n. 2 MAR 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
This paper studies the Cauchy problem on the line for the modified Korteweg-deVries equation whose dispersion is of order m = 2j + 1, where j >= 2 is a positive integer. Trilinear estimates in Bourgain spaces are proved and are used to show that local in time well-posedness holds in Sobolev spaces H-S for negative values of s. Then, using the analytic version of the trilinear estimates, well-posedness in a class of analytic functions on the line that can be extended holomorphically in a symmetric strip around the x-axis is proved. Finally, existence of global analytic solutions and a lower bound for the uniform radius of spatial analyticity are established. (AU) | |
| FAPESP's process: | 18/04950-7 - Global in time analytic solutions for the good Boussinesq equation and the nonlinear Schrödinger equation |
| Grantee: | RAFAEL FERNANDO BAROSTICHI |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 15/24109-7 - Analytic and Gevrey well-posedness of the "good" Boussinesq equation |
| Grantee: | Renata de Oliveira Figueira |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 17/12499-0 - Analytic and Gevrey well-posedness for the "good" Boussinesq equation |
| Grantee: | Renata de Oliveira Figueira |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |