On the L2L^{2}-critical nonlinear Schrödinger Equation with a nonlinear damping.

We consider the Cauchy problem for the $L^{2}$-critical nonlinear Schr\"{o}dinger equation with a nonlinear damping. According to the power of the damping term, we prove the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed for $\|\nabla u(t)\|_{L^2}$

On the well-posedness for Kadomtsev-Petviashvili-Burgers I equation.

International audienceWe prove local and global well-posedness in $H^{s,0}(\mathbb{R}^{2})$, $s > -\frac{1}{2}$, for the Cauchy problem associated with the Kadomotsev-Petviashvili-Burgers-I equation (KPBI) by working in Bourgain's type spaces. This result is almost sharp if one requires the flow-map to be smooth

Cost-Efficient Storage for On-Demand Video Streaming on Cloud

Video stream is converted to several formats to support the user's device, this conversion process is called video transcoding, which imposes high storage and powerful resources. With emerging of cloud technology, video stream companies adopted to process video on the cloud. Generally, many formats of the same video are made (pre-transcoded) and streamed to the adequate user's device. However, pre-transcoding demands huge storage space and incurs a high-cost to the video stream companies. More importantly, the pre-transcoding of video streams could be hierarchy carried out through different storage types in the cloud. To minimize the storage cost, in this paper, we propose a method to store video streams in the hierarchical storage of the cloud. Particularly, we develop a method to decide which video stream should be pre-transcoded in its suitable cloud storage to minimize the overall cost. Experimental simulation and results show the effectiveness of our approach, specifically, when the percentage of frequently accessed videos is high in repositories, the proposed approach minimizes the overall cost by up to 40 percent.Comment: International IEEE World Forum for Internet of Thing

Propagation of polarization sets for systems of MHD type

Polarization sets were introduced by Dencker (1982) as a refinement of wavefront sets to the vector-valued case. He also clarified the propagation of polarization sets when the characteristic variety of the pseudodifferential system under study consists of two hypersurfaces intersecting tangentially (1992), or transversally (1995). In this paper, we consider the case of more than two intersecting characteristic hypersurfaces that are interesting transversally (and we give a note on the tangential case). Mainly, we consider two types of systems which we name "systems of generalized transverse type" and "systems of MHD type", and we show that we can get a result for the propagation of polarization set similar to Dencker's result for systems of transverse type. Furthermore, we give an application to the MHD equations