618 research outputs found
A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation
We prove that every weak solution to the 3D Navier-Stokes equation that
belongs to the class and \n u belongs to localy
away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized
energy equality. In particular every such solution is suitable.Comment: 10 page
On admissibility criteria for weak solutions of the Euler equations
We consider solutions to the Cauchy problem for the incompressible Euler
equations satisfying several additional requirements, like the global and local
energy inequalities. Using some techniques introduced in an earlier paper we
show that, for some bounded compactly supported initial data, none of these
admissibility criteria singles out a unique weak solution.
As a byproduct we show bounded initial data for which admissible solutions to
the p-system of isentropic gas dynamics in Eulerian coordinates are not unique
in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof
Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time
The solutions of incompressible Navier-Stokes equations in four spatial
dimensions are considered. We prove that the two-dimensional Hausdorff measure
of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is
added in Remark 1.3. accepted by Comm. Math. Phy
The "Symplectic Camel Principle" and Semiclassical Mechanics
Gromov's nonsqueezing theorem, aka the property of the symplectic camel,
leads to a very simple semiclassical quantiuzation scheme by imposing that the
only "physically admissible" semiclassical phase space states are those whose
symplectic capacity (in a sense to be precised) is nh + (1/2)h where h is
Planck's constant. We the construct semiclassical waveforms on Lagrangian
submanifolds using the properties of the Leray-Maslov index, which allows us to
define the argument of the square root of a de Rham form.Comment: no figures. to appear in J. Phys. Math A. (2002
On the notion of phase in mechanics
The notion of phase plays an esential role in both classical and quantum
mechanics.But what is a phase? We show that if we define the notion of phase in
phase (!) space one can very easily and naturally recover the Heisenberg-Weyl
formalism; this is achieved using the properties of the Poincare-Cartan
invariant, and without making any quantum assumption
Comparative Analysis of the Mechanisms of Fast Light Particle Formation in Nucleus-Nucleus Collisions at Low and Intermediate Energies
The dynamics and the mechanisms of preequilibrium-light-particle formation in
nucleus-nucleus collisions at low and intermediate energies are studied on the
basis of a classical four-body model. The angular and energy distributions of
light particles from such processes are calculated. It is found that, at
energies below 50 MeV per nucleon, the hardest section of the energy spectrum
is formed owing to the acceleration of light particles from the target by the
mean field of the projectile nucleus. Good agreement with available
experimental data is obtained.Comment: 23 pages, 10 figures, LaTeX, published in Physics of Atomic Nuclei
v.65, No. 8, 2002, pp. 1459 - 1473 translated from Yadernaya Fizika v. 65,
No. 8, 2002, pp. 1494 - 150
About Starobinsky inflation
It is believed that soon after the Planck era, space time should have a
semi-classical nature. According to this, the escape from General Relativity
theory is unavoidable. Two geometric counter-terms are needed to regularize the
divergences which come from the expected value. These counter-terms are
responsible for a higher derivative metric gravitation. Starobinsky idea was
that these higher derivatives could mimic a cosmological constant. In this work
it is considered numerical solutions for general Bianchi I anisotropic
space-times in this higher derivative theory. The approach is ``experimental''
in the sense that there is no attempt to an analytical investigation of the
results. It is shown that for zero cosmological constant , there are
sets of initial conditions which form basins of attraction that asymptote
Minkowski space. The complement of this set of initial conditions form basins
which are attracted to some singular solutions. It is also shown, for a
cosmological constant that there are basins of attraction to a
specific de Sitter solution. This result is consistent with Starobinsky's
initial idea. The complement of this set also forms basins that are attracted
to some type of singular solution. Because the singularity is characterized by
curvature scalars, it must be stressed that the basin structure obtained is a
topological invariant, i.e., coordinate independent.Comment: Version accepted for publication in PRD. More references added, a few
modifications and minor correction
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