New analytic solutions of the non-relativistic hydrodynamical equations

Abstract

New solutions are found for the non-relativistic hydrodynamical equations. These solutions describe expanding matter with a Gaussian density profile. In the simplest case, thermal equilibrium is maintained without any interaction, the energy is conserved, and the process is isentropic. More general solutions are also obtained that describe explosions driven by heat production, or contraction of the matter caused by energy loss.

6 pages, LaTeX. Submitted to Physics Letters B. Shortened from 9 pages, errors corrected in the "More general solutions" section

Cited by in corpus (34)

• Hydrodynamic Approaches in Relativistic Heavy Ion Reactions
• On freeze-out problem in hydro-kinetic approach to A+A collisions
• Dissipation and elliptic flow at RHIC
• Simple solutions of relativistic hydrodynamics for systems with ellipsoidal symmetry
• Simple solutions of relativistic hydrodynamics for longitudinally and cylindrically expanding systems
• Lévy-stable two-pion Bose-Einstein correlations in $\sqrt{s_{{}_{NN}}}=200$ GeV Au$+$Au collisions
• Correlation femtoscopy
• Femtoscopic scales in $p+p$ and $p+$Pb collisions in view of the uncertainty principle
• Observables and initial conditions for self-similar ellipsoidal flows
• Simple solutions of fireball hydrodynamics for self-similar elliptic flows
• Back-to-Back Correlations for Finite Expanding Fireballs
• Phase-space densities and effects of resonance decays in hydrodynamic approach to heavy ion collisions
• Generating new solutions for relativistic transverse flow at the softest point
• Analytic solution for relativistic transverse flow at the softest point
• Squeezed K^+ K^- correlations in high energy heavy ion collisions
• Event-by-event investigation of the two-particle source function in heavy-ion collisions with EPOS
• New simple explicit solutions of perfect fluid hydrodynamics and phase-space evolution
• A new family of exact and rotating solutions of fireball hydrodynamics
• Novel self-similar rotating solutions of non-ideal transverse magnetohydrodynamics
• Inflation of fireballs, the gluon wind and the homogeneity of the HBT radii at RHIC
• New exact solutions of relativistic hydrodynamics for longitudinally expanding fireballs
• Simple analytic solution of fireball hydrodynamics
• The reconstructed final state of Au + Au collisions from PHENIX and STAR data at sqrt{s}=130 AGeV - indication for quark deconfinement at RHIC
• Lifetime estimations from RHIC Au+Au data
• Observables and initial conditions for rotating and expanding fireballs with spheroidal symmetry
• Anomalous radial expansion in central heavy-ion reactions
• Simple solutions of fireball hydrodynamics for rotating and expanding triaxial ellipsoids and final state observables
• Are back-to-back particle--antiparticle correlations observable in high energy nuclear collisions?
• Scaling properties of spectra in new exact solutions of rotating, multi-component fireball hydrodynamics
• Evolution of Observables in a Numerical Kinetic Model
• Acoustic horizons in nuclear fluids
• Space-time structure of particle emission and femtoscopy scales in ultrarelativistic heavy-ion collisions
• On the determinations of the size and shape of the interaction region from Bose-Einstein correlations
• New, spherical solutions of non-relativistic, dissipative hydrodynamics