Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  derive the one-dimensional (1D) isentropic Euler and Navier--Stokes equations describing the motion of a gas through a nozzle of variable cross section as the asymptotic limit of the 3D isentropic Navier--Stokes system in a cylinder, the diameter of which tends to zero. Our method is based on the relative energy inequality satisfied by any ak solution of the 3D Navier--Stokes system and a variant of the Korn--Poincare inequality on thin channels that may be of independent interest.
['Peter Bella', 'Eduard Feireisl', 'Marta Lewicka', 'Antonin Novotny']
I am writing a research paper on a idea A rigorous justification of the Euler and Navier-Stokes equations with geometric effects
[{"from": "human", "value": "I am writing a research paper on a idea A rigorous justification of the Euler and Navier-Stokes equations with geometric effects"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  derive the one-dimensional (1D) isentropic Euler and Navier--Stokes equations describing the motion of a gas through a nozzle of variable cross section as the asymptotic limit of the 3D isentropic Navier--Stokes system in a cylinder, the diameter of which tends to zero. Our method is based on the relative energy inequality satisfied by any ak solution of the 3D Navier--Stokes system and a variant of the Korn--Poincare inequality on thin channels that may be of independent interest."}]