# Estimate of $\Vert \nabla u \Vert_{L^{\infty}(\Omega)}$ of Navier Stokes equations

My question is how to estimate the term $$\Vert \nabla u \Vert_{L^{\infty}(\Omega)}$$. Here we consider the 2D incompressible Navier Stokes equations:$$u_t -\Delta u+u\cdot \nabla u+\nabla p=f$$ and $$\nabla \cdot u=0.$$ $$\Omega$$ is a bounded domain in $$\mathbb R^2$$ with no-slip boundary condition. Since we are considering on a bounded domain, we can no longer consider the vorticity equation. I appreciate if some reference papers are pointed out. Thanks.