Singular solutions, symmetries and self-similarity for PDEs

• Grant number: 10/19098-2
• Support Opportunities: Regular Research Grants
• Start date: March 01, 2011
• End date: February 28, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Lucas Catão de Freitas Ferreira
• Grantee: Lucas Catão de Freitas Ferreira
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project we will address the following kinds of nonlinear partial differential equations: Elliptic, parabolic with a singular nonlinearity, dispersive, and wave equation. We will study issues as existence of solutions without Sobolev regularity, nonradial self-similarity, invariance under certain kinds of rotations, blow-up, and asymptotic behavior. The basic strategy is to study those equations in suitable low-regularity functional spaces that allow to obtain solutions with the desired properties. (AU)

Scientific publications

(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)

FERREIRA, LUCAS C. F.. On a bilinear estimate in weak-Morrey spaces and uniqueness for Navier-Stokes equations. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 105, n. 2, p. 228-247, FEB 2016. (10/19098-2)

FERREIRA, LUCAS C. F.; MEDEIROS, EVERALDO S.; MONTENEGRO, MARCELO. On the Laplace equation with a supercritical nonlinear Robin boundary condition in the half-space. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 47, n. 3-4, p. 667-682, JUL 2013. (10/19098-2)