64 research outputs found
On the 2d Zakharov system with L^2 Schr\"odinger data
We prove local in time well-posedness for the Zakharov system in two space
dimensions with large initial data in L^2 x H^{-1/2} x H^{-3/2}. This is the
space of optimal regularity in the sense that the data-to-solution map fails to
be smooth at the origin for any rougher pair of spaces in the L^2-based Sobolev
scale. Moreover, it is a natural space for the Cauchy problem in view of the
subsonic limit equation, namely the focusing cubic nonlinear Schroedinger
equation. The existence time we obtain depends only upon the corresponding
norms of the initial data - a result which is false for the cubic nonlinear
Schroedinger equation in dimension two - and it is optimal because
Glangetas-Merle's solutions blow up at that time.Comment: 30 pages, 2 figures. Minor revision. Title has been change
Scattering for the Zakharov system in 3 dimensions
We prove global existence and scattering for small localized solutions of the
Cauchy problem for the Zakharov system in 3 space dimensions. The wave
component is shown to decay pointwise at the optimal rate of t^{-1}, whereas
the Schr\"odinger component decays almost at a rate of t^{-7/6}.Comment: Minor changes and referee's comments include
On the Cauchy problem for the magnetic Zakharov system
In this paper, we study the Cauchy problem of the magnetic type Zakharov
system which describes the pondermotive force and magnetic field generation
effects resulting from the non-linear interaction between plasma-wave and
particles. By using the energy method to derive a priori bounds and an
approximation argument for the construction of solutions, we obtain local
existence and uniqueness results for the magnetic Zakharov system in the case
of
Evaluarea şi monitorizarea rezultatelor obţinute în tratamentul fracturilor maleolare prin diferite tehnici în secţia ambulatorie de ortopedie şi traumatologie nr. 1
Studiul dat prezintă rezultatele la distanţă ale 580 de pacienţi cu fracturi maleolare, repartizaţi în două loturi conform metodelor de tratament, trataţi în cadrul CNŞPMU, secţia ambulatorie de ortopedie şi traumatologie nr. 1. Dintre ei, 459 pacienţi trataţi conservator, 121– chirurgical
Local well-posedness for the space-time Monopole equation in Lorenz gauge
It is known from the work of Czubak that the space-time Monopole equation is
locally well-posed in the Coulomb gauge for small initial data in
for . Here we prove local well-posedness for
arbitrary initial data in with in the Lorenz gauge.Comment: To appear in NoDE
Invariance of the white noise for KdV
We prove the invariance of the mean 0 white noise for the periodic KdV.
First, we show that the Besov-type space \hat{b}^s_{p, \infty}, sp <-1,
contains the support of the white noise. Then, we prove local well-posedness in
\hat{b}^s_{p, \infty} for p= 2+, s = -{1/2}+ such that sp <-1. In establishing
the local well-posedness, we use a variant of the Bourgain spaces with a
weight. This provides an analytical proof of the invariance of the white noise
under the flow of KdV obtained in Quastel-Valko.Comment: 18 pages. To appear in Comm. Math. Phy
On the ill-posedness result for the BBM equation
We prove that the initial value problem (IVP) for the BBM equation is
ill-posed for data in Hs(R), s < 0 in the sense that the ow-map u0 7! u(t) that
associates to initial data u0 the solution u cannot be continuous at the origin from
Hs(R) to even D0(R) at any _xed t > 0 small enough. This result is sharp.Fundação para a Ciência e a Tecnologia (FCT
Genomic insights into the origin of farming in the ancient Near East
We report genome-wide ancient DNA from 44 ancient Near Easterners ranging in time between ~12,000 and 1,400 BC, from Natufian hunter–gatherers to Bronze Age farmers. We show that the earliest populations of the Near East derived around half their ancestry from a ‘Basal Eurasian’ lineage that had little if any Neanderthal admixture and that separated from other non-African lineages before their separation from each other. The first farmers of the southern Levant (Israel and Jordan) and Zagros Mountains (Iran) were strongly genetically differentiated, and each descended from local hunter–gatherers. By the time of the Bronze Age, these two populations and Anatolian-related farmers had mixed with each other and with the hunter–gatherers of Europe to greatly reduce genetic differentiation. The impact of the Near Eastern farmers extended beyond the Near East: farmers related to those of Anatolia spread westward into Europe; farmers related to those of the Levant spread southward into East Africa; farmers related to those of Iran spread northward into the Eurasian steppe; and people related to both the early farmers of Iran and to the pastoralists of the Eurasian steppe spread eastward into South Asia
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