118 research outputs found
Dissipative continuous Euler flows
We show the existence of continuous periodic solutions of the 3D
incompressible Euler equations which dissipate the total kinetic energy
Asymptotic stability of the Cauchy and Jensen functional equations
The aim of this note is to investigate the asymptotic stability behaviour of
the Cauchy and Jensen functional equations. Our main results show that if these
equations hold for large arguments with small error, then they are also valid
everywhere with a new error term which is a constant multiple of the original
error term. As consequences, we also obtain results of hyperstability character
for these two functional equations
Weak Solutions to the Stationary Incompressible Euler Equations
We consider weak stationary solutions to the incompressible Euler equations
and show that the analogue of the h-principle obtained in [5, 7] for
time-dependent weak solutions continues to hold. The key difference arises in
dimension d = 2, where it turns out that the relaxation is strictly smaller
than what one obtains in the time-dependent case.Comment: 16 pages, 2 figures. Corrected a mistake in the proof of Theorem 17.
Results unchanged. Corrected a typographical erro
h-Principles for the Incompressible Euler Equations
Recently, De Lellis and Sz\'ekelyhidi constructed H\"older continuous,
dissipative (weak) solutions to the incompressible Euler equations in the torus
. The construction consists in adding fast oscillations to the
trivial solution. We extend this result by establishing optimal h-principles in
two and three space dimensions. Specifically, we identify all subsolutions
(defined in a suitable sense) which can be approximated in the -norm by
exact solutions. Furthermore, we prove that the flows thus constructed on
are genuinely three-dimensional and are not trivially obtained
from solutions on .Comment: 29 pages, no figure
Some functional equations related to the characterizations of information measures and their stability
The main purpose of this paper is to investigate the stability problem of
some functional equations that appear in the characterization problem of
information measures.Comment: 36 pages. arXiv admin note: text overlap with arXiv:1307.0657,
arXiv:1307.0631, arXiv:1307.0664, arXiv:1307.065
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