Some aspects of relativistic motion that depends on one spatial variable

Abstract

Specific relativistic effects associated with the instability of potential motions that depend on one spatial variable, including the instability of isentropic flows with respect to solenoidal perturbations, are considered. A general theorem is proved. Estimates and solutions are obtained in limiting cases of the separate action of the various effects of relativity and in the absence of other nonlinear hydrodynamic effects. It is shown that many already known solutions of the equations of relativistic hydrodynamics are unstable with respect to the development of transverse solenoidal components of the velocity.