Weighted Low-Regularity Solutions of the KP-I Initial Value Problem

In this paper we establish local well-posedness of the KP-I problem, with initial data small in the intersection of the natural energy space with the space of functions which are square integrable when multiplied by the weight y. The result is proved by the contraction mapping principle. A similar (but slightly weaker) result was the main Theorem in the paper " Low regularity solutions for the Kadomstev-Petviashvili I equation " by Colliander, Kenig and Staffilani (GAFA 13 (2003),737-794 and math.AP/0204244). Ionescu found a counterexample (included in the present paper) to the main estimate used in the GAFA paper, which renders incorrect the proof there. The present paper thus provides a correct proof of a strengthened version of the main result in the GAFA paper

Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations

In this paper, we consider Hartree-type equations on the two-dimensional torus and on the plane. We prove polynomial bounds on the growth of high Sobolev norms of solutions to these equations. The proofs of our results are based on the adaptation to two dimensions of the techniques we previously used to study analogous problems on $S^1$, and on $\mathbb{R}$.Comment: 38 page

Synthesizing SMOS Zero-Baselines with Aquarius Brightness Temperature Simulator

SMOS [1] and Aquarius [2] are ESA and NASA missions, respectively, to make L-band measurements from the Low Earth Orbit. SMOS makes passive measurements whereas Aquarius measures both passive and active. SMOS was launched in November 2009 and Aquarius in June 2011.The scientific objectives of the missions are overlapping: both missions aim at mapping the global Sea Surface Salinity (SSS). Additionally, SMOS mission produces soil moisture product (however, Aquarius data will eventually be used for retrieving soil moisture too). The consistency of the brightness temperature observations made by the two instruments is essential for long-term studies of SSS and soil moisture. For resolving the consistency, the calibration of the instruments is the key. The basis of the SMOS brightness temperature level is the measurements performed with the so-called zero-baselines [3]; SMOS employs an interferometric measurement technique which forms a brightness temperature image from several baselines constructed by combination of multiple receivers in an array; zero-length baseline defines the overall brightness temperature level. The basis of the Aquarius brightness temperature level is resolved from the brightness temperature simulator combined with ancillary data such as antenna patterns and environmental models [4]. Consistency between the SMOS zero-baseline measurements and the simulator output would provide a robust basis for establishing the overall comparability of the missions

Global well-posedness for a coupled modified kdv system

We prove the sharp global well-posedness result for the initial value problem (IVP) associated to the system of the modi ed Korteweg-de Vries (mKdV) equation. For the single mKdV equation such result has been obtained by using Mirura's Transform that takes the KdV equation to the mKdV equation [8]. We do not know the existence of Miura's Transform that takes a KdV system to the system we are considering. To overcome this di culty we developed a new proof of the sharp global well-posedness result for the single mKdV equation without using Miura's Transform. We could successfully apply this technique in the case of the mKdV system to obtain the desired result.Fundação para a Ciência e a Tecnologia (FCT

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

Residual stress determination by neutron diffraction in powder bed fusion-built Alloy 718: Influence of process parameters and post-treatment

Alloy 718 is a nickel-based superalloy that is widely used as a structural material for high-temperature applications. One concern that arises when Alloy 718 is manufactured using powder bed fusion (PBF) is that residual stresses appear due to the high thermal gradients. These residual stresses can be detrimental as they can degrade mechanical properties and distort components. In this work, residual stresses in PBF built Alloy 718, using both electron and laser energy sources, were measured by neutron diffraction. The effects of process parameters and thermal post-treatments were studied. The results show that thermal post-treatments effectively reduce the residual stresses present in the material. Moreover, the material built with laser based PBF showed a higher residual stress compared to the material built with electron-beam based PBF. The scanning strategy with the lower amount of residual stresses in case of laser based PBF was the chessboard strategy compared to the bi-directional raster strategy. In addition, the influence of measured and calculated lattice spacing (d0) on the evaluated residual stresses was investigated

Development of SMAP Mission Cal/Val Activities

The Soil Moisture Active Passive (SMAP) mission is a NASA directed mission to map global land surface soil moisture and freeze-thaw state. Instrument and mission details are shown. The key SMAP soil moisture product is provided at 10 km resolution with 0.04cubic cm/cubic cm accuracy. The freeze/thaw product is provided at 3 km resolution and 80% frozen-thawed classification accuracy. The full list of SMAP data products is shown

The dynamics of the 3D radial NLS with the combined terms

In this paper, we show the scattering and blow-up result of the radial solution with the energy below the threshold for the nonlinear Schr\"{o}dinger equation (NLS) with the combined terms iu_t + \Delta u = -|u|^4u + |u|^2u \tag{CNLS} in the energy space $H^1(\R^3)$. The threshold is given by the ground state $W$ for the energy-critical NLS: $iu_t + \Delta u = -|u|^4u$. This problem was proposed by Tao, Visan and Zhang in \cite{TaoVZ:NLS:combined}. The main difficulty is the lack of the scaling invariance. Illuminated by \cite{IbrMN:f:NLKG}, we need give the new radial profile decomposition with the scaling parameter, then apply it into the scattering theory. Our result shows that the defocusing, $\dot H^1$-subcritical perturbation $|u|^2u$ does not affect the determination of the threshold of the scattering solution of (CNLS) in the energy space.Comment: 46page

A para-differential renormalization technique for nonlinear dispersive equations

For \alpha \in (1,2) we prove that the initial-value problem \partial_t u+D^\alpha\partial_x u+\partial_x(u^2/2)=0 on \mathbb{R}_x\times\mathbb{R}_t; u(0)=\phi, is globally well-posed in the space of real-valued L^2-functions. We use a frequency dependent renormalization method to control the strong low-high frequency interactions.Comment: 42 pages, no figure