189,324 research outputs found
Compressible Navier-Stokes equations without heat conduction in Lp-framework
In this paper, we mainly consider global well-posedness and long time
behavior of compressible Navier-Stokes equations without heat conduction in
-framework. This is a generalization of Peng and Zhai \cite{peng}(SIMA,
55(2023), no.2, 1439-1463), where they obtained the corresponding result in
-framework. Based on the key observation that we can release the
regularity of non-dissipative entropy in high frequency in \cite{peng}, we
ultimately achieve the desired estimate in the high frequency via
complicated calculations on the nonlinear terms. In addition, we get the
-decay rate of the solution.Comment: arXiv admin note: text overlap with arXiv:2308.1638
Two approximations to the bound states of Dirac-Hulthen problem
The bound state (energy spectrum and two-spinor wave functions) solutions of
the Dirac equation with the Hulthen potential for all angular momenta based on
the spin and pseudospin symmetry are obtained. The parametric generalization of
the Nikiforov-Uvarov method is used in the calculations. The orbital dependency
(spin-orbit and pseudospin-orbit dependent coupling too singular 1/r^{2}) of
the Dirac equation are included to the solution by introducing a more accurate
approximation scheme to deal with the centrifugal (pseudo-centrifugal) term.
The approximation is also made for the less singular 1/r orbital term in the
Dirac equation for a wider energy spectrum. The nonrelativistic limits are also
obtained on mapping of parameters.Comment: 29 pages, 7 figures. arXiv admin note: text overlap with
arXiv:hep-th/050320
A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity
The Aviles Giga functional is a well known second order functional that forms
a model for blistering and in a certain regime liquid crystals, a related
functional models thin magnetized films. Given Lipschitz domain the functional is where belongs to the subset of
functions in whose gradient (in the sense of trace)
satisfies where is the inward pointing unit
normal to at . In Jabin, Otto, Perthame characterized a
class of functions which includes all limits of sequences with as . A
corollary to their work is that if there exists such a sequence for a
bounded domain , then must be a ball and (up to change of
sign) .
Recently we provided a quantitative generalization of this corollary over the
space of convex domains using `compensated compactness' inspired calculations
originating from the proof of coercivity of by DeSimone, Muller,
Kohn, Otto. In this note we use methods of regularity theory and ODE to provide
a sharper estimate and a much simpler proof for the case where
without the requiring the trace condition on .Comment: 16 pages, 1 figur
Microscopic Origin of Criticality at Macroscale in QCD Chiral Phase Transition
We reveal that the criticality of the chiral phase transition in QCD at the
macroscale arises from the microscopic energy levels of its fundamental
constituents, the quarks. We establish a novel relation between cumulants of
the chiral order parameter (i.e., chiral condensate) and correlations among the
energy levels of quarks (i.e., eigenspectra of the massless Dirac operator),
which naturally leads to a generalization of the Banks-Casher relation. Based
on this novel relation and through (2+1)-flavor lattice QCD calculations using
the HISQ action with varying light quark masses in the vicinity of the chiral
phase transition, we demonstrate that the correlations among the infrared part
of the Dirac eigenspectra exhibit same universal scaling behaviors as expected
of the cumulants of the chiral condensate. We find that these universal scaling
behaviors extend up to the physical values of the up and down quark masses.Comment: 4 pages, 2 figures, talk presented at the 30th International
Conference on Ultra-relativistic Nucleus-Nucleus Collisions (Quark Matter
2023), September 3-9, 2023, Houston, Texas, USA. arXiv admin note: text
overlap with arXiv:2401.1026
New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models
We propose a hypothesis on the detailed structure for the representation of
the conformal symmetry breaking term in the basic Crewther relation generalized
in the perturbation theory framework in QCD renormalized in the scheme. We establish the validity of this representation in the
approximation. Using the variant of the generalized Crewther
relation formulated here allows finding relations between specific
contributions to the QCD perturbation series coefficients for the flavor
nonsinglet part of the Adler function for the electron-positron
annihilation in hadrons and to the perturbation series coefficients for the
Bjorken sum rule for the polarized deep-inelastic lepton-nucleon
scattering. We find new relations between the coefficients of
and . Satisfaction of one of them serves as an
additional theoretical verification of the recent computer analytic
calculations of the terms of order in the expressions for these
two quantities.Comment: 12 pages, Title modified, abstract modified, improved and extended
variant of the talks, presented at Int. Seminar "Quarks-2010" (6-12 June,
2010, Kolomna) and Int. Workshop Hadron Structure and QCD: From Low to High
Energies (5-9 July 2010, Gatchina
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