Minimal set of differential invariants of an extended loop group arising in fluid flows

• Grant number: 18/21330-2
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: February 01, 2019
• End date: July 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Alexandre Grichkov
• Grantee: Alexandre Grichkov
• Visiting researcher: Vladimir Grebenev
• Visiting researcher institution: Siberian Branch of the Russian Academy of Sciences (SB RAS), Russia
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project is devoted to one of the problems that occupied the researchers working in the area of Lie algebras at the turn of the last century, one can identify with generating the minimal set of diýerential invariants for Lie (pseudo-)group actions. The fundamental basis theorem states that all diýerential invariants can be generated from a nite number of low order invariants by repeated invariant diýerentiation. This theorem rst formulated by Lie in the nite-dimensional Lie (pseudo-) groups, and then extended by Tresse to in nite dimensional Liepseudo-groups, states that the diýerential invariant algebra is nitely generated. The problem is to construct the minimal set of diýerential invariants for Lie (pseudo-) group actions. (AU)

Scientific publications

(4)

(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)

GREBENEV, VLADIMIR N.; DEMENKOV, ANDREW G.; CHERNYKH, GENNADY G.; GRICHKOV, ALEXANDRE N.. Local equilibrium approximation in free turbulent flows: Verification through the method of differential constrains. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, APR 2021. (18/21330-2)

GREBENEV, V. N.; WACLAWDZYK, M.; ODERLACK, M.. Conformal invariance of the zero-vorticity Lagrangian path in 2D turbulence. Journal of Physics A-Mathematical and Theoretical, v. 52, n. 33, AUG 16 2019. (18/21330-2)

GREBENEV, V. N.; GRICHKOV, A. N.; OBERLACK, M.; WACLAWCZYK, M.. Second-order invariants of the inviscid Lundgren-Monin-Novikov equations for 2d vorticity fields. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 72, n. 3, JUN 2021. (18/21330-2)

GREBENEV, VLADIMIR N.; DEMENKOV, ANDREW G.; CHERNYKH, GENNADY G.; GRICHKOV, ALEXANDRE N.. Local equilibrium approximation in free turbulent flows: Verification through the method of differential constrains. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, v. 101, n. 9, SEP 2021. (18/21330-2)