It is still not known whether a solution to the incompressible Euler equation, endowed with smooth initial value, can blow-up in finite time. In Vasseur and Vishik (2020) [17] it has been shown that, if exists, such becomes linearly unstable close this paper, we show that same phenomenon holds even more rigid axisymmetric case. To obtain result, first prove criterion involving only toroidal com...

If either finite electron inertia or finite resistivity is included in 2D magnetic reconnection, the two-fluid equations become a pair of second-order differential equations coupling the out-of-plane magnetic field and vector potential to each other to form a fourth-order system. The coupling at an X-point is such that out-of-plane even-parity electric and odd-parity magnetic fields feed off ea...

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis o...

Temperature or pressure anisotropies are characteristic of space plasmas, standard magnetohydrodynamic (MHD) model for describing large-scale plasma phenomena however usually assumes isotropic pressure. In this paper we examine the characteristics of MHD waves, fire-hose and mirror instabilities in anisotropic homogeneous magnetized plasmas. The model equations are a set of gyrotropic MHD equat...

The study sought to investigate thermosolutal convection and stability of two dimensional disturbances imposed on a heated boundary layer flow over a semi-infinite horizontal plate composed of a chemical species using a self-consistent asymptotic method. The chemical species reacts as it diffuses into the nearby fluid causing density stratification and inducing a buoyancy force. The existence o...

Stability properties of magnetic-field configurations containing the toroidal and axial field are considered. The stability is treated by making use of linear analysis. It is shown that the conditions required for the onset of instability are essentially different from those given by the necessary condition d(sBφ)/ds > 0, where s is the cylindrical radius. The growth rate of instability is calc...

An overview of recent experimental results on instability and dynamics of jets at low Reynolds numbers is given. Round and plane, macro and micro jets are under the consideration. Basic features of their evolution affected by initial conditions at the nuzzle outlet and environmental perturbations are demonstrated.

We study the interaction between dynamos with different spatial and temporal scales. In particular we consider cases in which the smaller of the dynamo systems is itself unstable to dynamo action. We find that the degree of interaction depends on the magnetic Reynolds number, and the relative amplitude between the driving velocities at different scales. Even though it is possible to construct c...

Abstract. The Benjamin-Feir instability describes the instability of a uniform oscillatory wave train in an irrotational flow subject to small perturbation of wave number, amplitude and frequency. Their instability analysis is based on the perturbation around the second order Stokes wave which satisfies the dynamic and kinematic free-surface boundary conditions up to the second order. In the sa...