Abstract In this paper, we consider the $L^2$-critical fractional Schrödinger equation $iu_t-|D|^{\beta }u+|u|^{2\beta }u=0$ with initial data $u_0\in H^{\beta /2}(\mathbb{R})$ and $\beta $ close to $2$. We show that if have negative energy slightly supercritical mass, then solution blows up in finite time. also give a specific description for blow-up dynamics. This is an extension of works F. ...

1.1.2 What is randomness? Successive observations, x(n-1), x(n), x(n+1), ... are dependent on one another • If x(n) can be predicted exactly from the previous samples then the time-series signal is deterministic • If x(n) cannot be predicted exactly from the previous samples the time-series signal is random or stochastic • If x(n) is independent from previous samples then the time-series signal...

In order to construct the border solutions for nonsupersingular elliptic curve equations, some common used models need to be adapted from linear treated cases for use in particular nonlinear cases. There are some approaches that conclude with these solutions. Optimization in this area means finding the majority of points on the elliptic curve and minimizing the time to compute the solution in c...

Let (M, g) be a closed locally conformally flat Riemannian manifold of dimension $$n \ge 7$$ and positive Yamabe type. If $$h \in C^1(M)$$ $$\xi _0$$ is non-degenerate critical point the mass function we prove existence, for any $$ k 1$$ blowing-up solution $$u_\varepsilon $$\begin{aligned} \triangle _g u_\varepsilon +\big ( c_n S_g +\varepsilon h\big ) = ^{2^*-1} \end{aligned}$$ that blows up,...

The three studies presented here aim to contribute to a better understanding of the role of the coordinate system of a person's body and of the environment in spatial organization underlying the recognition and production of gestures. The paper introduces a new approach by investigating what people consider to be opposite gestures in addition to identical gestures. It also suggests a new point ...

We consider a model equation for 3D vorticity dynamics of incompressible viscous fluid proposed by K. Ohkitani and the second author of the present paper. We prove that a solution blows up in finite time if the L1-norm of the initial vorticity is greater than the viscosity.

In this paper we consider the nonlinearly damped semilinear wave equation utt −∆u + aut |ut|m−2 = bu|u|p−2 associated with initial and Dirichlet boundary conditions. We prove that any strong solution, with negative initial energy, blows up in finite time if p > m. This result improves an earlier one in [2].