A group theoretical approach to hydrodynamics considers hydrodynamics to be the
differential geometry of diffeomorphism groups. The principle of least action implies that the …

Preface “... ad alcuno, dico, di quelli, che troppo laconicamente vorrebbero vedere, nei piu
angusti spazii che possibil fusse, ristretti i filosofici insegnamenti, sı che sempre si usasse …

Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper of V. Arnold.
In this paper we present a collection of open problems along with several new constructions …

This is a survey paper on the quantitative analysis of the propagation of singularities for the
viscosity solutions to Hamilton–Jacobi equations in the past decades. We also review further …

We develop a Lagrangian approach to conservation-law anomalies in weak solutions of
inviscid Burgers equation, motivated by previous work on the Kraichnan model of turbulent …

For autonomous Tonelli systems on R^ n R n, we develop an intrinsic proof of the existence
of generalized characteristics using sup-convolutions. This approach, together with …

Generalized solutions of the system of zero-pressure gas dynamics equations in the case of
two spatial variables are considered. In contrast to the much-studied case of one spatial …

Weak solutions of the system of pressureless gas dynamics equations in two dimensions are
studied. Theoretical issues are considered, namely, the general mathematical theory of …

Рассматриваются обобщенные решения системы уравнений газовой динамики без
давления в случае двух пространственных переменных. В отличие от много …

Система уравнений газовой динамики без давления представляет собой
гидродинамически обоснованное обобщение системы уравнений, состоящей из …