  We consider the Cauchy problem for the isentropic compressible Euler
equations in a three-dimensional periodic domain under general pressure laws.
For any smooth initial density away from the vacuum, we construct infinitely
many entropy solutions with no presence of shock. In particular, the
constructed density is smooth and the momentum is $\alpha$-H\"older continuous
for $\alpha<1/7$. Also, we provide a continuous entropy solution satisfying the
entropy inequality strictly.
