This question is somewhat related to the these questions:-Is Gauss' law valid for time-dependent electric fields? and Gauss's law for induced electric and magnetic field
But my question is somewhat different from the above.If a system of charges enclosed in gaussian surface is accelerated then can we accelerate our gaussian surface in same direction to make Gauss's law valid for accelerating charges as well.Is it true or completely nonsense?Does electric flux depends upon the motion of gaussian surface relative to charge enclosed?