1,662 research outputs found
The C^{\a} regularity of a class of ultraparabolic equations
We prove the regularity for weak solutions to a class of
ultraparabolic equation, with measurable coefficients. The results generalized
our recent regularity results of Prandtl's system to high
dimensional cases.Comment: 18 page
Landis-Oleinik Conjecture in the Exterior Domain
In 1974, Landis and Oleinik conjectured that if a bounded solution of a
parabolic equation decays fast at a time, then the solution must vanish
identically before that time, provided the coefficients of the equation satisfy
appropriate conditions at infinity. We prove this conjecture under some
reasonable assumptions on the coefficients which improved the earlier results.Comment: 34 page
regularity of weak solutions of non-homogenous ultraparabolic equations with drift terms
Consider a class of non-homogenous ultraparabolic differential equations with
drift terms or lower order terms arising from some physical models, and we
prove that weak solutions are H\"{o}lder continuous, which also generalizes the
classic results of parabolic equations of second order. The main ingredients
are a type of weak Poincar\'{e} inequality satisfied by non-negative weak
sub-solutions and Moser iteration.Comment: We delete the Prandtl part and add some details for
estimate. arXiv admin note: text overlap with arXiv:0711.341
H\"{o}lder Continuous Solutions Of Boussinesq Equation with compact support
We show the existence of Holder continuous solution of Boussinesq equations
in whole space which has compact support both in space and time.Comment: final versio
On the interior regularity criteria of the 3-D Navier-Stokes equations involving two velocity components
We present some interior regularity criteria of the 3-D Navier-Stokes
equations involving two components of the velocity. These results in particular
imply that if the solution is singular at one point, then at least two
components of the velocity have to blow up at the same point.Comment: 20 page
Backward uniqueness for parabolic operators with variable coefficients in a half space
It is shown that a function satisfying
,
in and in
under certain conditions on must vanish
identically in . The main point of the result is
that the conditions imposed on are of the type: are
Lipschitz and , where is less than
a given number, and the conditions are in some sense optimal.Comment: 32 page
Backward uniqueness for general parabolic operators in the whole space
We prove the backward uniqueness for general parabolic operators of second
order in the whole space under assumptions that the leading coefficients of the
operator are Lipschitz and their gradients satisfy certain decay conditions.
This result extends in some ways a classical result of Lions and Malgrange [12]
and a recent result of the authors [10]
Backward Uniqueness of Kolmogorov Operators
The backward uniqueness of the Kolmogorov operator
, was proved in this paper. We obtained a weak
Carleman inequality via Littlewood-Paley decomposition for the global backward
uniqueness.Comment: 10 page
On The Continuous Periodic Weak Slution of Boussinesq Equations
The Boussingesq equations was introduced in understanding the coupling nature
of the thermodynamics and the fluid dynamics. We show the existence of
continuous periodic weak solutions of the Boussinesq equations which satisfies
the prescribed kinetic energy or some other prescribed property. Our results
represent the conversions between internal energy and mechanical energy.Comment: 43 pages. Revised title and introducto
The geometric measure of entanglement of pure states with nonnegative amplitudes and the spectral theory of nonnegative tensors
The geometric measure of entanglement for a symmetric pure state with
nonnegative amplitudes has attracted much attention. On the other hand, the
spectral theory of nonnegative tensors (hypermatrices) has been developed
rapidly. In this paper, we show how the spectral theory of nonnegative tensors
can be applied to the study of the geometric measure of entanglement for a pure
state with nonnegative amplitudes. Especially, an elimination method for
computing the geometric measure of entanglement for symmetric pure multipartite
qubit or qutrit states with nonnegative amplitudes is given. For symmetric pure
multipartite qudit states with nonnegative amplitudes, a numerical algorithm
with randomization is presented and proven to be convergent. We show that for
the geometric measure of entanglement for pure states with nonnegative
amplitudes, the nonsymmetric ones can be converted to the symmetric ones.Comment: 21 page
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