Analytic and Gevrey well-posedness for the "good" Boussinesq equation

• Grant number: 17/12499-0
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: January 10, 2018
• End date: December 09, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: RAFAEL FERNANDO BAROSTICHI
• Grantee: Renata de Oliveira Figueira
• Supervisor: Alex Alexandrou Himonas
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: University of Notre Dame, United States
• Associated to the scholarship: 15/24109-7 - Analytic and Gevrey well-posedness of the "good" Boussinesq equation, BP.DR

Abstract

On both the circle and the line, we want to prove that the Cauchy problem for "good" Boussinesq equation is locally well-posed in a class of analytic functions that can be extended holomorphically in a symmetric strip of the complex plane around the x-axis. Also, we intend to prove that this equation is well-posed in Gevrey spaces. Finally, information about the regularity of the solution in the time variable shall be provided.

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BAROSTICHI, RAFAEL F.; FIGUEIRA, RENATA O.; HIMONAS, A. ALEXANDROU. Well-posedness of the ``good{''} Boussinesq equation in analytic Gevrey spaces and time regularity. Journal of Differential Equations, v. 267, n. 5, p. 3181-3198, AUG 15 2019. (18/04950-7, 17/12499-0, 15/24109-7)

FIGUEIRA, RENATA; HIMONAS, A. ALEXANDROU; YAN, FANGCHI. A higher dispersion KdV equation on the line. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 199, OCT 2020. (17/12499-0, 15/24109-7)

FIGUEIRA, RENATA O.; HIMONAS, A. ALEXANDROU. Lower bounds on the radius of analyticity for a system of modified KdV equations. Journal of Mathematical Analysis and Applications, v. 497, n. 2, MAY 15 2021. (17/12499-0, 15/24109-7)

BAROSTICHI, RAFAEL; FIGUEIRA, RENATA O.; HIMONAS, A. ALEXANDROU. The modified KdV equation with higher dispersion in Sobolev and analytic spaces on the line. JOURNAL OF EVOLUTION EQUATIONS, v. 21, n. 2, MAR 2021. (18/04950-7, 15/24109-7, 17/12499-0)

BAROSTICHI, RAFAEL F.; FIGUEIRA, RENATA O.; HIMONAS, A. ALEXANDROU. Well-posedness of the "good" Boussinesq equation in analytic Gevrey spaces and time regularity. Journal of Differential Equations, v. 267, n. 5, p. 18-pg., 2019-08-15. (17/12499-0, 18/04950-7, 15/24109-7)