# Electronic hydrodynamics in graphene

## TL;DR

This paper derives the unique electronic hydrodynamics of graphene using kinetic theory, including magnetic fields and dissipative properties, highlighting differences from traditional relativistic hydrodynamics.

## Contribution

It provides a pedagogical derivation of graphene's unconventional hydrodynamics, extending previous work to include magnetic fields and explicit dissipative coefficients.

## Key findings

- Derived explicit expressions for shear viscosity and electrical conductivity.
- Compared graphene hydrodynamics with relativistic hydrodynamics.
- Extended the theory to include external magnetic fields.

## Abstract

In this paper I report a pedagogical derivation of the unconventional electronic hydrodynamics in graphene on the basis of the kinetic theory. While formally valid in the weak coupling limit, this approach allows one to derive the unconventional hydrodynamics in the system which is neither Galilean- nor Lorentz-invariant, such that hydrodynamic equations can not be inferred from symmetry arguments. I generalize earlier work to include external magnetic fields and give explicit expressions for dissipative coefficients, the shear viscosity and electrical conductivity. I also compare the resulting theory with relativistic hydrodynamics.