On Blow-up criterion for the Nonlinear Schr\"{o}dinger Equation

The blowup is studied for the nonlinear Schr\"{o}dinger equation $iu_{t}+\Delta u+ |u|^{p-1}u=0$ with $p$ is odd and $p\ge 1+\frac 4{N-2}$ (the energy-critical or energy-supercritical case). It is shown that the solution with negative energy $E(u_0)<0$ blows up in finite or infinite time. A new proof is also presented for the previous result in \cite{HoRo2}, in which a similar result but more general in a case of energy-subcritical was shown.Comment: In this version, we add a reference, and change some expressions in Englis

Global solutions to the Nernst-Planck-Euler system on bounded domain

We show that the Nernst-Planck-Euler system, which models ionic electrodiffusion in fluids, has global strong solutions for arbitrarily large data in the two dimensional bounded domains. The assumption on species is either there are two species or the diffusivities and the absolute values of ionic valences are the same if the species are arbitrarily many. In particular, the boundary conditions for the ions are allowed to be inhomogeneous. The proof is based on the energy estimates, integration along the characteristic line and the regularity theory of elliptic and parabolic equations

Real-Time Parameter Identification for Forging Machine Using Reinforcement Learning

It is a challenge to identify the parameters of a mechanism model under real-time operating conditions disrupted by uncertain disturbances due to the deviation between the design requirement and the operational environment. In this paper, a novel approach based on reinforcement learning is proposed for forging machines to achieve the optimal model parameters by applying the raw data directly instead of observation window. This approach is an online parameter identification algorithm in one period without the need of the labelled samples as training database. It has an excellent ability against unknown distributed disturbances in a dynamic process, especially capable of adapting to a new process without historical data. The effectiveness of the algorithm is demonstrated and validated by a simulation of acquiring the parameter values of a forging machine