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Superfluid turbulence, often referred to as quantum turbulence, is a fascinating phenomenon for which a satisfactory theoretical framework is lacking. Holographic duality provides a systematic new approach to studying quantum turbulence by…
In this paper we investigate spectral stability of traveling wave solutions to 1-$D$ quantum hydrodynamics system with nonlinear viscosity in the $(\rho,u)$, that is, density and velocity, variables. We derive a sufficient condition for the…
In this paper we study concentrated solutions of the three-dimensional Euler equations in helical symmetry without swirl. We prove that any helical vorticity solution initially concentrated around helices of pairwise distinct radii remains…
The work analyzes the stability of the quantum eigenstates when they are submitted to fluctuations by using the stochastic generalization of the Madelung quantum hydrodynamic approach. In the limit of sufficiently slow kinetics, the quantum…
We study the spectrum of the linearization around standing wave profiles for two quantum hydrodynamics systems with linear and nonlinear viscosity. The essential spectrum for such profiles is stable; we investigate the point spectrum using…
Quantum hydrodynamic theory (QHT) can describe some of the characteristic features of quantum electron dynamics that appear in metallic nanostructures, such as spatial nonlocality, electron spill-out, and quantum tunneling. Furthermore,…
This study focuses on microscopic-sized quantum vortex filaments that are shaped like a circle. The model we considered examines loops with different radii and a small but non-zero core diameter. These loops are located in a bounded domain…
Axially symmetric solutions to the Navier-Stokes equations in a bounded cylinder are considered. On the boundary the normal component of the velocity and he angular components of the velocity and vorticity are assumed to vanish. If the norm…
The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging…
We find hydrodynamic behavior in large simply spinning five-dimensional Anti-de Sitter black holes. These are dual to spinning quantum fluids through the AdS/CFT correspondence constructed from string theory. Due to the spatial anisotropy…
Quantum fluid (or hydrodynamic) models provide an attractive alternative for the modeling and simulation of the electron dynamics in nano-scale objects. Compared to more standard approaches, such as density functional theory or phase-space…
We develop a many-particle quantum-hydrodynamical model of fermion matter interacting with the external classical electromagnetic and gravitational/inertial and torsion fields. The consistent hydrodynamical formulation is constructed for…
Rotating turbulence is ubiquitous in nature. Previous works suggest that such turbulence could be described as an ensemble of interacting inertial waves across a wide range of length scales. For turbulence in macroscopic quantum…
We study isolated, stationary, axially symmetric vortex solutions in (2+1)-dimensional viscous conformal fluids. The equations describing them can be brought to the form of three coupled first order ODEs for the radial and rotational…
The Madelung equations offer a hydrodynamic description of quantum systems, from single particles to quantum fluids. In this formulation, the probability density is mapped onto the fluid density and the phase is treated as a scalar…
The generalized transport equations for a consistent description of kinetic and hydrodynamic processes in dense gases and liquids are considered. The inner structure of the generalized transport kernels for these equations is established.…
We formulate a quantum theory of vorticity (hydro)dynamics on a general two-dimensional bosonic lattice. In the classical limit of a bosonic condensate, it reduces to conserved plasma-like vortex-antivortex dynamics. The nonlocal…
The conventional no-slip boundary condition leads to a non-integrable stress singularity at a contact line. This is a main challenge in numerical simulations of two-phase flows with moving contact lines. We derive a two-dimensional…
Strongly nonlinear dynamics, from fluid turbulence to quantum chromodynamics, have long constituted some of the most challenging problems in theoretical physics. This review describes a unified theoretical framework, the loop space…
We propose a mixed quantum-classical hydrodynamic framework to model short-time inertial effects in the non-adiabatic evolution of a quantum solute coupled to a classical polar solvent. Drawing upon the work of Burghardt and Bagchi [Chem.…