In this paper ##J=\frac{\partial f_1(X_1)}{\partial X_1}\frac{\partial f_2(X_2)}{\partial X_2}\frac{\partial f_3(X_3)}{\partial X_3}## where ##f_2(X_2),f_1(X_1),f_3(X_3)## evolves with time.

Now using this ##\dot J=\frac{d}{dt}(\frac{\partial f_1(X_1)}{\partial X_1}\frac{\partial f_2(X_2)}{\partial X_2}\frac{\partial f_3(X_3)}{\partial X_3})## and using ##\frac{d}{dt}=\frac{\partial}{\partial t}+(v•\nabla)## and ##\frac{\partial X_i}{\partial t}=0## this comes as ##3(v•\nabla)J## but it is given as ##J\theta## where ##\theta=\nabla • v##

Will anyone please help me in sort out this....

Now using this ##\dot J=\frac{d}{dt}(\frac{\partial f_1(X_1)}{\partial X_1}\frac{\partial f_2(X_2)}{\partial X_2}\frac{\partial f_3(X_3)}{\partial X_3})## and using ##\frac{d}{dt}=\frac{\partial}{\partial t}+(v•\nabla)## and ##\frac{\partial X_i}{\partial t}=0## this comes as ##3(v•\nabla)J## but it is given as ##J\theta## where ##\theta=\nabla • v##

Will anyone please help me in sort out this....

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