Hydrodynamic gradient expansion in linear response theory

Understand

A foundational question in relativistic fluid mechanics concerns the properties of the hydrodynamic gradient expansion at large orders.

• We establish the precise conditions under which this gradient expansion diverges for a broad class of microscopic theories admitting a relativistic hydrodynamic limit, in the linear regime.
• Our result does not rely on highly symmetric fluid flows utilized by previous studies of heavy-ion collisions and cosmology.
• The hydrodynamic gradient expansion diverges whenever energy density or velocity fields have support in momentum space exceeding a critical momentum, and converges otherwise.