64 research outputs found

    On the 2d Zakharov system with L^2 Schr\"odinger data

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    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

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    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

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    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 d=2,3d=2,3

    Evaluarea şi monitorizarea rezultatelor obţinute în tratamentul fracturilor maleolare prin diferite tehnici în secţia ambulatorie de ortopedie şi traumatologie nr. 1

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    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

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    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 Hs(R2)H^s(\mathbb{R}^2) for s>1/4s>1/4. Here we prove local well-posedness for arbitrary initial data in Hs(R2)H^s(\mathbb{R^2}) with s>1/4s>1/4 in the Lorenz gauge.Comment: To appear in NoDE

    Invariance of the white noise for KdV

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    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

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    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

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    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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