Shock waves for the Burgers equation and curvatures of diffeomorphism groups

DOI10.1134/S0081543807040062zbMath1161.35464arXivmath/0702196MaRDI QIDQ2377582

Gerard Misiołek, Boris A. Khesin

Publication date: 19 January 2009

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702196

zbMATH Keywords

Burgers equationshock wavesdiffeomorphism groups

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Interfacial stability and instability in hydrodynamic stability (76E17) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (6)

Singularities of \(A\) and \(B\) types in asymptotic analysis of solutions of a parabolic equation ⋮ A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers' equation ⋮ Geometric hydrodynamics in open problems ⋮ Asymptotic Solutions of a Parabolic Equation Near Singular Points of A and B Types ⋮ On dynamics of Lagrangian trajectories for Hamilton-Jacobi equations ⋮ Differential Geometric Heuristics for Riemannian Optimal Mass Transportation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Perestroikas of shocks and singularities of minimum functions
• Asymptotic directions, Monge-Ampère equations and the geometry of diffeomorphism groups
• For ideal fluids, Eulerian and Lagrangian instabilities are equivalent
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Groups of diffeomorphisms and the motion of an incompressible fluid
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Burgulence
• Polar factorization of maps on Riemannian manifolds

This page was built for publication: Shock waves for the Burgers equation and curvatures of diffeomorphism groups