94 research outputs found
Recent Advances Concerning Certain Class of Geophysical Flows
This paper is devoted to reviewing several recent developments concerning
certain class of geophysical models, including the primitive equations (PEs) of
atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for
large-scale oceanic and atmospheric dynamics are derived from the Navier-Stokes
equations coupled to the heat convection by adopting the Boussinesq and
hydrostatic approximations, while the tropical atmosphere model considered here
is a nonlinear interaction system between the barotropic mode and the first
baroclinic mode of the tropical atmosphere with moisture.
We are mainly concerned with the global well-posedness of strong solutions to
these systems, with full or partial viscosity, as well as certain singular
perturbation small parameter limits related to these systems, including the
small aspect ratio limit from the Navier-Stokes equations to the PEs, and a
small relaxation-parameter in the tropical atmosphere model. These limits
provide a rigorous justification to the hydrostatic balance in the PEs, and to
the relaxation limit of the tropical atmosphere model, respectively. Some
conditional uniqueness of weak solutions, and the global well-posedness of weak
solutions with certain class of discontinuous initial data, to the PEs are also
presented.Comment: arXiv admin note: text overlap with arXiv:1507.0523
Quantitative uniqueness for elliptic equations with singular lower order terms
We use a Carleman type inequality of Koch and Tataru to obtain quantitative
estimates of unique continuation for solutions of second order elliptic
equations with singular lower order terms. First we prove a three sphere
inequality and then describe two methods of propagation of smallness from sets
of positive measure.Comment: 23 pages, v2 small changes are done and some mistakes are correcte
Uncertainty estimates and L_2 bounds for the Kuramoto-Sivashinsky equation
We consider the Kuramoto-Sivashinsky (KS) equation in one spatial dimension
with periodic boundary conditions. We apply a Lyapunov function argument
similar to the one first introduced by Nicolaenko, Scheurer, and Temam, and
later improved by Collet, Eckmann, Epstein and Stubbe, and Goodman, to prove
that ||u||_2 < C L^1.5. This result is slightly weaker than that recently
announced by Giacomelli and Otto, but applies in the presence of an additional
linear destabilizing term. We further show that for a large class of Lyapunov
functions \phi the exponent 1.5 is the best possible from this line of
argument. Further, this result together with a result of Molinet gives an
improved estimate for L_2 boundedness of the Kuramoto-Sivashinsky equation in
thin rectangular domains in two spatial dimensions.Comment: 17 pages, 1 figure; typos corrected, references added; figure
modifie
WHEAT STRAW CONVERSION BY ENZYMATIC SYSTEM OF GANODERMA LUCIDUM
The purpose of this study was to resolve the question of whether various nitrogen sources and concentrations affect characteristics of selected G. lucidum ligninolytic enzymes participating in wheat straw fermentation. This is the first study reporting the presence of versatile peroxidase activity in crude extract of G. lucidum culture, as well as isoforms profile of Mn-oxidizing peroxidases. NH4NO3 was the optimum nitrogen source for laccase and Mn-dependent peroxidase activity, while peptone was the optimum one for versatile peroxidase activity. Four bands with laccase activity were obtained by native PAGE and IEF separations from medium enriched with inorganic nitrogen source, and only two bands from medium containing organic source. Medium composition was not shown to affect isoenzyme patterns of Mn-oxidizing peroxidases. Four isoforms of Mn-dependent peroxidase and three of versatile peroxidase were obtained on native PAGE. By IEF separation, five isoforms of Mn-dependent peroxidase and only two of versatile peroxidase were observed. The results demonstrated that G. lucidum has potential for mineralization and transformation of various agricultural residues and should take more significant participation in large-scale biotechnological processes
Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise
The Primitive Equations are a basic model in the study of large scale Oceanic
and Atmospheric dynamics. These systems form the analytical core of the most
advanced General Circulation Models. For this reason and due to their
challenging nonlinear and anisotropic structure the Primitive Equations have
recently received considerable attention from the mathematical community.
In view of the complex multi-scale nature of the earth's climate system, many
uncertainties appear that should be accounted for in the basic dynamical models
of atmospheric and oceanic processes. In the climate community stochastic
methods have come into extensive use in this connection. For this reason there
has appeared a need to further develop the foundations of nonlinear stochastic
partial differential equations in connection with the Primitive Equations and
more generally.
In this work we study a stochastic version of the Primitive Equations. We
establish the global existence of strong, pathwise solutions for these
equations in dimension 3 for the case of a nonlinear multiplicative noise. The
proof makes use of anisotropic estimates, estimates on the
pressure and stopping time arguments.Comment: To appear in Nonlinearit
Existence of global strong solutions to a beam-fluid interaction system
We study an unsteady non linear fluid-structure interaction problem which is
a simplified model to describe blood flow through viscoleastic arteries. We
consider a Newtonian incompressible two-dimensional flow described by the
Navier-Stokes equations set in an unknown domain depending on the displacement
of a structure, which itself satisfies a linear viscoelastic beam equation. The
fluid and the structure are fully coupled via interface conditions prescribing
the continuity of the velocities at the fluid-structure interface and the
action-reaction principle. We prove that strong solutions to this problem are
global-in-time. We obtain in particular that contact between the viscoleastic
wall and the bottom of the fluid cavity does not occur in finite time. To our
knowledge, this is the first occurrence of a no-contact result, but also of
existence of strong solutions globally in time, in the frame of interactions
between a viscous fluid and a deformable structure
Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array
In this paper we investigate the asymptotic validity of boundary layer
theory. For a flow induced by a periodic row of point-vortices, we compare
Prandtl's solution to Navier-Stokes solutions at different numbers. We
show how Prandtl's solution develops a finite time separation singularity. On
the other hand Navier-Stokes solution is characterized by the presence of two
kinds of viscous-inviscid interactions between the boundary layer and the outer
flow. These interactions can be detected by the analysis of the enstrophy and
of the pressure gradient on the wall. Moreover we apply the complex singularity
tracking method to Prandtl and Navier-Stokes solutions and analyze the previous
interactions from a different perspective
The Inviscid Limit and Boundary Layers for Navier-Stokes Flows
The validity of the vanishing viscosity limit, that is, whether solutions of
the Navier-Stokes equations modeling viscous incompressible flows converge to
solutions of the Euler equations modeling inviscid incompressible flows as
viscosity approaches zero, is one of the most fundamental issues in
mathematical fluid mechanics. The problem is classified into two categories:
the case when the physical boundary is absent, and the case when the physical
boundary is present and the effect of the boundary layer becomes significant.
The aim of this article is to review recent progress on the mathematical
analysis of this problem in each category.Comment: To appear in "Handbook of Mathematical Analysis in Mechanics of
Viscous Fluids", Y. Giga and A. Novotn\'y Ed., Springer. The final
publication is available at http://www.springerlink.co
Nonlinear Instability for the Critically Dissipative Quasi-Geostrophic Equation
We prove that linear instability implies non-linear instability in the energy
norm for the critically dissipative quasi-geostrophic equation.Comment: 16 pages, corrected typos, a global bound that was obtained for the
unforced equation by Kiselev-Nazarov-Volberg obtained for the forced equation
and utilized in the paper
Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids
Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold
(M,g). In this paper we study the restrictions on the topology and geometry of
the fibres (the level sets) of the solutions f to (P1). We give a technique
based on certain remarkable property of the fibres (the analytic representation
property) for going from the initial PDE to a global analytical
characterization of the fibres (the equilibrium partition condition). We study
this analytical characterization and obtain several topological and geometrical
properties that the fibres of the solutions must possess, depending on the
topology of M and the metric tensor g. We apply these results to the classical
problem in physics of classifying the equilibrium shapes of both Newtonian and
relativistic static self-gravitating fluids. We also suggest a relationship
with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis
is proved. Please address all correspondence to D. Peralta-Sala
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