Velocity Averaging Lemmas for equations with rough coefficients

• Grant number: 25/12847-5
• Support Opportunities: Scholarships abroad - Research
• Start date: March 02, 2026
• End date: March 01, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: João Fernando da Cunha Nariyoshi
• Grantee: João Fernando da Cunha Nariyoshi
• Host Investigator: Pierre Emmanuel Jabin
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Pennsylvania State University, United States

Abstract

We will investigate ``velocity averaging lemmas'' for classes of equations whose coefficients are less regular than those in the classical theory of Lions-Perthame-Tadmor. Consequently, via kinetic formulations, such results will yield new regularity theorems for scalar conservation laws that have remained little studied so far. We will also analyze extensions of these results to cases with spatially nonhomogeneous coefficients and to second-order equations. The project will be carried out in collaboration with Prof. Pierre-Emmanuel Jabin(PennState, USA).