128 research outputs found
On the flow map for 2D Euler equations with unbounded vorticity
In Part I, we construct a class of examples of initial velocities for which
the unique solution to the Euler equations in the plane has an associated flow
map that lies in no Holder space of positive exponent for any positive time. In
Part II, we explore inverse problems that arise in attempting to construct an
example of an initial velocity producing an arbitrarily poor modulus of
continuity of the flow map.Comment: http://iopscience.iop.org/0951-7715/24/9/013/ for published versio
Interaction of vortices in viscous planar flows
We consider the inviscid limit for the two-dimensional incompressible
Navier-Stokes equation in the particular case where the initial flow is a
finite collection of point vortices. We suppose that the initial positions and
the circulations of the vortices do not depend on the viscosity parameter \nu,
and we choose a time T > 0 such that the Helmholtz-Kirchhoff point vortex
system is well-posed on the interval [0,T]. Under these assumptions, we prove
that the solution of the Navier-Stokes equation converges, as \nu -> 0, to a
superposition of Lamb-Oseen vortices whose centers evolve according to a
viscous regularization of the point vortex system. Convergence holds uniformly
in time, in a strong topology which allows to give an accurate description of
the asymptotic profile of each individual vortex. In particular, we compute to
leading order the deformations of the vortices due to mutual interactions. This
allows to estimate the self-interactions, which play an important role in the
convergence proof.Comment: 39 pages, 1 figur
Global well-posedness issues for the inviscid Boussinesq system with Yudovich's type data
The present paper is dedicated to the study of the global existence for the
inviscid two-dimensional Boussinesq system. We focus on finite energy data with
bounded vorticity and we find out that, under quite a natural additional
assumption on the initial temperature, there exists a global unique solution.
None smallness conditions are imposed on the data. The global existence issues
for infinite energy initial velocity, and for the B\'enard system are also
discussed.Comment: 12 page
On the analyticity and Gevrey class regularity up to the boundary for the Euler Equations
We consider the Euler equations in a three-dimensional Gevrey-class bounded
domain. Using Lagrangian coordinates we obtain the Gevrey-class persistence of
the solution, up to the boundary, with an explicit estimate on the rate of
decay of the Gevrey-class regularity radius
Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation
Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion
Recently, there has been a wide interest in the study of aggregation
equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate
diffusion. The focus of this paper is the unification and generalization of the
well-posedness theory of these models. We prove local well-posedness on bounded
domains for dimensions and in all of space for , the
uniqueness being a result previously not known for PKS with degenerate
diffusion. We generalize the notion of criticality for PKS and show that
subcritical problems are globally well-posed. For a fairly general class of
problems, we prove the existence of a critical mass which sharply divides the
possibility of finite time blow up and global existence. Moreover, we compute
the critical mass for fully general problems and show that solutions with
smaller mass exists globally. For a class of supercritical problems we prove
finite time blow up is possible for initial data of arbitrary mass.Comment: 31 page
Mercury release and speciation in chemical looping combustion of coal
In the in situ Gasification Chemical Looping Combustion of coal (iG-CLC), the fuel is gasified
in situ in the fuel reactor and gasification products are converted to CO2 and H2O by reaction
with the oxygen carrier. This work is the first study on mercury release in Chemical Looping
Combustion of coal. The fraction of the mercury in coal vaporized in the fuel reactor depended
mainly on the fuel reactor temperature and the coal type. In the fuel reactor, mercury was mainly
emitted as Hg0 in the gas phase and the amount increased with the temperature. In the air reactor,
mercury was mostly emitted as Hg2+. In a real CLC system, mercury emissions to the
atmosphere will decrease compared to conventional combustion as only mercury released in the
air reactor will reach the atmosphere. However, measures should be taken to reduce Hg0 in the
CO2 stream before the purification and compression steps in order to avoid operational problems.The authors thank the Government of Aragón and La Caixa (2012-GA-LC-076 project) and the Spanish Ministry for Science and Innovation (ENE2010-19550 project) for the financial support. P. Gayán thanks CSIC for the financial support of the project 201180E102. The authors also thank to Alcoa Europe-Alúmina Española S.A. for providing the Fe-enriched sand fraction used in this work. G. Galo is acknowledged for his contribution to the experimental results.Peer reviewe
Existence and uniqueness for stochastic 2D Euler flows with bounded vorticity
The strong existence and the pathwise uniqueness of solutions with (Formula presented.) -vorticity of the 2D stochastic Euler equations are proved. The noise is multiplicative and it involves the first derivatives. A Lagrangian approach is implemented, where a stochastic flow solving a nonlinear flow equation is constructed. The stability under regularizations is also proved
Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
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