4D-Flow MRI is a technique used to measure blood velocity by applicating approppriate magnetic gradients to a patient lying in a magnetic resonance scanner. This is a non-invasive technique that is useful for the diagnosis of cardiovascular diseases. In this work, we are interested in two difficulties of the technique: the noise and an artifact known as aliasing due to the phase-contrast nature of the velocity estimation, since the measured phases live in a given interval, their contrast can be wrapped. These limitations pose a trade-off problem in the acquisition design. In this work, we use physics-informed neural networks for mitigating the noise and also for unwrapping aliased velocities, mitigating the trade-off problem. 1. We study how applying physical constraints can denoise 4D-Flow MRI images. We start with the case of an MSE data loss, establishing a bound that prevents the neural network from fitting the noisy data more than needed. 2. Then, we introduce a data loss that allows unwrapping. This data loss is nonconvex, and we show a strategy for falling into the good local minima, and so correctly unwrapping. This strategy allows denoising at the same time, and we establish a bound for this data loss to avoid fitting noise. The physical constraints in the study come from the Navier-Stokes equations: the momentum equation, the incompressibility condition, and also an augmentation of Navier-Stokes for improving the PINNs performance. We show numerical experiments that motivate the applicability of the method for velocity correction. This work is funded by PUCV VINCI-DI 039.728/2025.