Estimates on solution of pde

Question

Let's consider the following pde in $\mathbb{R}^n$ $$\partial_t u=(i+\varepsilon)\Delta u,\,\,\,u(0,x)=u_0(x)$$ How to get the following estimate for its solution? $$\Vert u\Vert_2\leq C_\varepsilon t^{-\frac{1}{4}}\Vert u_0\Vert_{\frac{3}{2}}$$ ($\Vert f\Vert_p$ is the $L^p$ norm)