- Jan 2018 – April 2018, 6th Semester Project at NISER,
- Guide: Dr. Victor Roy, School of Physical Sciences, NISER
Abstract: Fluidity is an ubiquitous property encountered frequently in many physical systems and at various energy scales. In the non-relativistic limit, there is a well understood formalism to understand
uid properties. In the present project,the formalism to understand ideal fluids, which do not dissipate, is
discussed. The applications of these equations is illustrated for different cases such as hydrostatics, the case of incompressible fluids etc. In order to take dissipation into account Navier-Stokes equation is used, which is an extension of the Euler equation. It is shown that the the kinetic energy density of the
uid decreases with time as a result of the dissipative term in Navier-Stokes equation. At higher energy scales the relativistic effects needs to be taken into account. Equations for relativistic ideal fluid dynamics have been discussed. It is shown that it reduces to the continuity equation and Euler equation in the non-relativistic limit. But generalising Navier-Stokes Equation leads to the problem of acausality. There are different approaches to incorporate causality into the theory of relativistic hydrodynamics. Theresults of Maxwell-Cattaneo approach and Muller-Israel-Stewart approach are discussed, and it is shown how the equations obtained by these methods respects causality.