16 citations · 48 across the 14 of their papers we have counts for
14 papers
On the catastrophe time of fluids under the action of a gravitational field
D. Astesiano, G. Ortenzi, M. L. Ruggiero
Motivated by the central role of the Zel'dovich approximation in the description of cosmic structure formation through gravitational collapse, we investigate Burgers-type dynamics…
On Euler equation for incoherent fluid in curved spaces
B. G. Konopelchenko, G. Ortenzi
Hodograph equations for the Euler equation in curved spaces with constant pressure are discussed. It is shown that the use of known results concerning geodesics and associated inte…
On pressureless Euler equation with external force
B. G. Konopelchenko, G. Ortenzi
Hodograph equations for the n-dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Eule…
Homogeneous Euler equation: blow-ups, gradient catastrophes and singularity of mappings
B. G. Konopelchenko, G. Ortenzi
The paper is devoted to the analysis of the blow-ups of derivatives, gradient catastrophes and dynamics of mappings of associated with the -dimen…
On universality of homogeneous Euler equation
B. G. Konopelchenko, G. Ortenzi
Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions pr…
Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach
R. Camassa, G. Falqui, G. Ortenzi
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler syste…
Jordan form, parabolicity and other features of change of type transition for hydrodynamic type systems
B. G. Konopelchenko, G. Ortenzi
Changes of type transitions for the two-component hydrodynamic type systems are discussed. It is shown that these systems generically assume the Jordan form (with 2 X 2 Jordan bloc…
Cohomological, Poisson structures and integrable hierarchies in tautological subbundles for Birkhoff strata of Sato Grassmannian
B. G. Konopelchenko, G. Ortenzi
Cohomological and Poisson structures associated with the special tautological subbundles for the Birkhoff strata of Sato Grassmannian are considered. It is s…
Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems
B. G. Konopelchenko, G. Ortenzi
Structure and properties of families of critical points for classes of functions obeying the elliptic Euler-Poisson-Darboux equation are studied. Genera…
Quasi-classical approximation in vortex filament dynamics. Integrable systems, gradient catastrophe and flutter
B. G. Konopelchenko, G. Ortenzi
Quasiclassical approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this approximation the governing equations are given by elliptic syst…
Gradient catastrophe and flutter in vortex filament dynamics
B. G. Konopelchenko, G. Ortenzi
Gradient catastrophe and flutter instability in the motion of vortex filament within the localized induction approximation are analyzed. It is shown that the origin if this phenome…
Algebraic varieties in Birkhoff strata of the Grassmannian Gr: Harrison cohomology and integrable systems
B. G. Konopelchenko, G. Ortenzi
Local properties of families of algebraic subsets in Birkhoff strata of Gr containing hyperelliptic curves of genus are studied. It is shown that the tan…
Birkhoff strata of the Grassmannian Gr: Algebraic curves
B. G. Konopelchenko, G. Ortenzi
Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian Gr are studied. It is shown that the big cell contains the tower of families of t…
Hamiltonian motions of plane curves and formation of singularities and bubbles
B. G. Konopelchenko, G. Ortenzi
A class of Hamiltonian deformations of plane curves is defined and studied. Hamiltonian deformations of conics and cubics are considered as illustrative examples. These deformation…