This paper presents a derivation of nonlinear equations of boundary fluid dynamics from gravity using the AdS/CFT correspondence. The authors study black branes in AdS5, which are described by four parameters: velocity and temperature. By promoting these parameters to Goldstone modes or collective coordinate fields, they use Einstein's equations and boundary conditions to determine the dynamics of these fields. The resulting equations are found to be those of boundary fluid dynamics with specific values for fluid parameters. The analysis is perturbative in the boundary derivative expansion but valid for arbitrary amplitudes. The work provides a systematic framework to construct nonlinear fluid dynamics order by order in a boundary derivative expansion. The authors derive the stress tensor of the fluid to second order in the derivative expansion, showing that it is Weyl invariant. The results are consistent with previous studies and provide new insights into the behavior of strongly coupled conformal field theories. The paper also discusses the implications of these results for the study of fluid dynamics and gravitational systems.This paper presents a derivation of nonlinear equations of boundary fluid dynamics from gravity using the AdS/CFT correspondence. The authors study black branes in AdS5, which are described by four parameters: velocity and temperature. By promoting these parameters to Goldstone modes or collective coordinate fields, they use Einstein's equations and boundary conditions to determine the dynamics of these fields. The resulting equations are found to be those of boundary fluid dynamics with specific values for fluid parameters. The analysis is perturbative in the boundary derivative expansion but valid for arbitrary amplitudes. The work provides a systematic framework to construct nonlinear fluid dynamics order by order in a boundary derivative expansion. The authors derive the stress tensor of the fluid to second order in the derivative expansion, showing that it is Weyl invariant. The results are consistent with previous studies and provide new insights into the behavior of strongly coupled conformal field theories. The paper also discusses the implications of these results for the study of fluid dynamics and gravitational systems.