Maximal L1L_1-regularity of the Navier-Stokes equations with free boundary conditions via a generalized semigroup theory

This paper develops a unified approach to show the maximal regularity theorem of the Stokes equations with free boundary conditions in the half-space $\mathbb R^d_+$, $d \ge 2$, within the $L_1$-in-time and $\mathcal B^s_{q, 1}$-in-space framework with $(q, s)$ satisfying $1 < q < \infty$ and $- 1 + 1 / q < s < 1 / q$, where $\mathcal B^s_{q, 1}$ stands for either homogeneous or inhomogeneous Besov spaces. In particular, we establish a generalized semigroup theory within an $L_1$-in-time and $\mathcal B^s_{q,1}$-in-space framework, which extends a classical $C_0$-analytic semigroup theory to the case of inhomogeneous boundary conditions. The maximal $L_1$-regularity theorem is proved by estimating the Fourier-Laplace inverse transform of the solution to the generalized Stokes resolvent problem with inhomogeneous boundary conditions, where density and interpolation arguments are used. The maximal $L_1$-regularity theorem is applied to show the unique existence of a local strong solution to the Navier-Stokes equations with free boundary conditions for arbitrary initial data $\boldsymbol a$ in $B^s_{q, 1} (\mathbb R^d_+)^d$, where $q$ and $s$ satisfy $d-1 < q \le d$ and $-1+d/q < s < 1/q$, respectively. If we assume that the initial data $\boldsymbol a$ are small in $\dot{B}^{- 1 + d / q}_{q, 1} (\mathbb R^d_+)^d$, $d - 1 < q < 2 d$, then the unique existence of a global strong solution to the system is proved.Comment: The result on the local well-posedness and its proof are correcte

Velocity Structure of Jets in Coronal Hole

Velocity structures of jets in a coronal hole have been derived for the first time. Hinode observations revealed the existence of many bright points in coronal holes. They are loop-shaped and sometimes associated with coronal jets. Spectra obtained with the Extreme ultraviolet Imaging Spectrometer (EIS) on board Hinode are analyzed to infer Doppler velocity of bright loops and jets in a coronal hole of the north polar region. Elongated jets above bright loops are found to be blue-shifted by 30 km/s at maximum, while foot points of bright loops are red-shifted. Blue-shifts detected in coronal jets are interpreted as upflows produced by magnetic reconnection between emerging flux and the ambient field in the coronal hole.Comment: 11 pages, 7 figures, accepted for publication in PASJ Hinode special issu

Framework for virtual collaboration emphasized by awareness information and asynchronous interaction

ICME2008 : IEEE International Conference on Multimedia and Expo , Jun 23-26, 2008 , Hannover, GermanyIn this paper, we propose a framework which allows remote users to form conversation groups based on spatial relationship in a shared virtual space. Our proposed framework can transport awareness information of real world by capturing and transferring user’s audio visual information. Our framework also provides functions useful to CSCW, which allow each user to simultaneously join different conversation groups, and communicate with others asynchronously exchanging awareness information. We show a reference implementation architecture to realize the framework in an ordinary computing and networking environment

An Energy-Aware Video Streaming System for Portable Computing Devices

MDM'06 : 7th International Conference on Mobile Data Management , May 9-12, 2006 , Nara, JapanIn this demonstration, we show an energy-aware video streaming system which allows users to play back video for the specified duration within the remaining battery amount. In the system, we execute a proxy server on an intermediate node in the network. It receives the video stream from a content server, transcodes it to the videos with appropriate quality, and forwards it to a PDA or a laptop PC. Here, suitable parameter values of the video (such as picture size, frame rate and bitrate) which enable playback for the specified duration are automatically calculated on the proxy using our battery consumption model. The system also allows users to play back video segments with different qualities based on the importance specified to each video segment