Related papers: Irregular shock waves formation as continuation of…

The spontaneous emission of internal waves (IWs) from balanced mesoscale eddies has been previously proposed to provide a source of oceanic IW kinetic energy (KE). This study examines the mechanisms leading to the spontaneous emission of…

We examine the stability of self-similar solutions for an accelerating relativistic blast wave which is generated by a point explosion in an external medium with a steep radial density profile of a power-law index > 4.134. These…

Shock tubes have been a crucial device, facilitating studies across a wide range of practical applications. An open-ended shock tube employing the wire-explosion technique with a rectangular cross section is used in the present study to…

Various formal blow-up scenarious for the Navier--Stokes equaitons in 3D are discussed. A particular interest is payed to "twistor mechanisms" based on angular logarithmic blow-up travelling waves, and to a formation of "blow-up tornado"…

The phenomenon of bursting, in which streaks in turbulent boundary layers oscillate and then eject low speed fluid away from the wall, has been studied experimentally, theoretically, and computationally for more than 50 years because of its…

The perturbed Burgers and KdV equations are considered. Often, the perturbation excites waves that are different from the solution one is seeking. In the case of the Burgers equation, the spontaneously generated wave is also a solution of…

This paper deals with the blow-up properties of positive solutions to a system of two heat equations.

Recent works have demonstrated that continuous self-similar radial Euler flows can drive primary (non-differentiated) flow variables to infinity at the center of motion. Among the variables that blow up at collapse is the pressure, and it…

The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in…

Spiral wave patterns observed in models of cardiac arrhythmias and chemical oscillations develop alternans and stationary line defects, which can both be thought of as period-doubling instabilities. These instabilities are observed on…

We study interfacial instabilities between two spatially periodically sheared ideal fluids. Bloch wavefunction decompositions of the surface deformation and fluid velocities result in a nonhermitian secular matrix with an associated band…

The term "solid-state turbulence" may sound like an oxymoron, but in fact it is not. In this article we demonstrate that solid-state turbulence may emerge owing to a defining property of the solid state: the ability of a solid to retain its…

We consider in this paper a large class of perturbed semilinear wave equations with critical (in the conformal transform sense) power nonlinearity. We will show that the blow-up rate of any singular solution is given by the solution of the…

The collision of a plane parallel shock wave with a plane parallel cloud of uniform density is analysed for the case in which magnetic fields and radiative losses are not considered. General analytic solutions are discussed for the case in…

This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to discuss which of the new directions they have taken…

We consider co-rotational wave maps from (1+3)-dimensional Minkowski space into the three-sphere. This model exhibits an explicit blowup solution and we prove the asymptotic nonlinear stability of this solution in the whole space under…

We investigate the blow-up dynamics of smooth solutions to the one-dimensional wave equation with a quadratic spatial derivative nonlinearity, motivated by its applications in Effective Field Theory (EFT) in cosmology. Despite its…

We consider the corrugation instability of the self-similar flow with an accelerating shock in the highly relativistic regime. We derive the correct dispersion relation for the proper modes in the self-similar regime, and conclude that this…

In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equation has solutions which show characteristics…

The structure of steady plane-parallel radiative shock waves propagating through the hydrogen gas undergoing partial ionization and excitation of bound atomic states is investigated in terms of the self-consistent solution of the equations…