Related papers: Cauchy Problem for Cylinder-like Capillary Jets
This paper is concerned with the well-posedness theory of the impact of a subsonic axially symmetric jet emerging from a semi-infinitely long nozzle, onto a rigid wall. The fluid motion is described by the steady isentropic Euler system. We…
A wide class of exact solutions is obtained for the problem of finding the equilibrium configurations of charged jets of a conducting liquid; these configurations correspond to the finite-amplitude azimuthal deformations of the surface of a…
The Plateau-Rayleigh theory essentially explains the breakup of liquid jets as due to growing perturbations along the length of the jet. The essential idea is supported by several experiments carried out in the past. Recently, the existence…
In the classical survey (Chapter 16.2, {\it Mathematics in industrial problem}, Vol. 24, Springer-Verlag, New York, 1989), A. Friedman proposed an open problem on the collision of two incompressible jets emerging from two axially symmetric…
Recent experimental studies on the instability appearance of capillary jets have revealed the capabilities of linear spatiotemporal instability analysis to predict the parametrical map where steady jetting or dripping takes place. In this…
We consider the Cauchy problem associated to the recently derived higher order hamiltonian model for unidirectional water waves and prove global existence for given data in the Sobolev space $H^s$, $s\geq 1$. We also prove an ill-posedness…
A simple, intuitive, and low-cost setup for generating and measuring capillary waves is presented enabling a precise determination of the dispersion relation for a cylindrical water jet. By setting the phase velocity and measuring the…
Numerical studies of dimple and jet formation from a collapsing cavity often model the initial cavity shape as a truncated sphere, mimicking a bursting bubble. In this study, we present a minimal model containing only nonlinear inertial and…
This article represents a first step towards understanding the well-posedness for the dispersive Hunter-Saxton equation. This problem arises in the study of nematic liquid crystals, and although the equation has formal similarities with the…
The Cauchy problem for the three-dimensional compressible flow of nematic liquid crystals is considered. Existence and uniqueness of the global strong solution are established in critical Besov spaces provided that the initial datum is…
We revisit the classic problem of the stability of drops and jets held by surface tension, while regarding the compressibility of bulk fluids and spatial dimensions as free parameters. By mode analysis, it is shown that there exists a…
We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono equation \[\partial_t u+|\partial_x|^{1+\alpha}\partial_x u+uu_x=0,\ u(x,0)=u_0(x),\] is locally well-posed in the Sobolev spaces $H^s$ for $s>1-\alpha$ if $0\leq…
In this paper, we establish the existence of three-dimensional axisymmetric compressible jet flows for steady Euler system with large vorticity by using the variational method. More precisely, for given axial velocity of the flow at the…
In this Brief Communication we study experimentally the flow regimes that appear in co-axial air-water jets discharging into a stagnant air atmosphere and we propose a simple explanation for their occurrence based on linear, local,…
In this paper, we consider the Cauchy problem for a class of weakly dissipative Camassa-Holm equations in nonhomogeneous Besov spaces. First, we prove that the Cauchy problem admits a unique global strong solution in Besov spaces with…
We consider a quasilinear parabolic Cauchy problem with spatial anisotropy of orthotropic type and study the spatial localization of solutions. Assuming the initial datum is localized with respect to a coordinate having slow diffusion rate,…
This paper deals with the existence and uniqueness of solutions to kinetic equations describing alignment of self-propelled particles. The particularity of these models is that the velocity variable is not on the euclidean space but…
This paper is concerned with the Cauchy problem of the one-dimensional free surface equation of shallow water wave, we obtain local well-posedness of the free surface equation of shallow water wave in Sobolev spaces. In addition, we also…
We investigate the equations of anisotropic axisymmetric incompressible viscous fluids in the exterior of a cylinder of $\R^3$, rotating around an inhomogeneous vector $B(t, r)$. We prove uniform local existence with respect to the Rossby…
A fluid jet with a finite angular velocity is subject to centripetal forces in addition to surface tension forces. At fixed angular momentum, centripetal forces become large when the radius of the jet goes to zero. We study the possible…