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In this paper, we show the shock formation of the solutions to the3-dimensional (3D) compressible isentropic and irrotational Euler equationswith damping for the initial short pulse data which was first introduced byD.Christodoulou\cite{christodoulou2007}. Due to the damping effect, thelargeness of the initial data is necessary for the shock formation and we willwork on the class of large data (in energy sense). Similar to the undampedcase, the formation of shock is characterized by the collapse of thecharacteristic hypersurfaces and the vanishing of the inverse foliation densityfunction $\mu$, at which the first derivatives of the velocity and the densityblow up. However, the damping effect changes the asymptotic behavior of theinverse foliation density function $\mu$ and then shifts the time of shockformation compared with the undamped case. The methods in the paper can also beextended to a class of $3D$ quasilinear wave equations for the short pulseinitial data.

Formation of shifted shock for the 3D compressible Euler equations with damping