Unilateral Problem for a Viscoelastic Beam Equation Type p-Laplacian with Strong Damping and Logarithmic Source

In this manuscript, we investigate the unilateral problem for a viscoelastic beam equation of p-Laplacian type. The competition of the strong damping versus the logarithmic source term is considered. We use the potential well theory. Taking into account the initial data is in the stability set created by the Nehari surface, we prove the existence and uniqueness of global solutions by using the penalization method and Faedo-Galerkin’s approximation.

On the absence of global solutions to two-times-fractional differential inequalities involving Hadamard-Caputo and Caputo fractional derivatives

<abstract><p>In this paper, we consider a two-times nonlinear fractional differential inequality involving both Hadamard-Caputo and Caputo fractional derivatives of different orders, with a singular potential term. We obtain sufficient criteria depending on the parameters of the problem, for which a global solution does not exist. Some examples are provided to support our main results.</p></abstract>

Global well-posedness for the 3D magneto-micropolar equations with fractional dissipation

This paper focus on the Cauchy problem of the 3D incompressible magneto-micropolar equations with fractional dissipation in the Sobolev space. Liu, Sun and Xin obtained the global solutions to the 3D magneto-micropolar equations with $\alpha=\beta=\gamma=\frac{5}{4}$. Deng and Shang established the global well-posedness of the 3D magneto-micropolar equations in the case of $\alpha\geq\frac{5}{4}$, $\alpha+\beta\geq\frac{5}{2}$ and $\gamma\geq2-\alpha\geq\frac{3}{4}$. In this paper, we establish the global well-posedness of the 3D magneto-micropolar equations with $\alpha=\beta=\frac{5}{4}$ and $\gamma=\frac{1}{2}$, which improves the results of Liu-Sun-Xin and Deng-Shang by reducing the value of $\gamma$ to $\frac{1}{2}$.

The Legal Status of “Migrants” according to the European Union Legislation

Given that “migration” is a global phenomenon, the international community as a whole had to provide it with a legal basis and to find global solutions, as proven à l’évidence by both the international and the European legislation and the “Global Compact for Migration” approved by the European Council. As is well known, the European Union legislation consists of the texts of its official instruments, such as conventions, treaties, declarations, etc., in which we also find, in fact, the principles stated in the international instruments, which have, indeed, the force of jus cogens for all the states of the world, concerning the universal human rights, including, thus, the rights of the migrants. However, even in terms of their policy regarding migrants, the member states of the European Union have not only applied the principles stated in these international instruments, but they also have enacted a special legislation, and they have taken concrete measures for the implementation of its rules. In the present article I offer the reader the possibility to become acquainted not only with the text of the legislation of the European Union regarding migrants, but also with the policy and the actions taken by the European states for the implementation of the international legislation, and of the European one regarding the social rights of the migrants as workers.