Interest in 4D blood flow MRI grows due to its ability to image the anatomic shape and the three velocity components within a volume along the cardiac cycle. However, some biomarkers' quantification from these data can be inaccurate due to the low resolution of the images. The reference method to improve the spatial resolution numerically is to run computational fluid dynamic (CFD) simulations in order to deduce the associated images in a higher resolution grid. However, such approaches induce complex time-consuming steps and require precise estimates of the vessel wall and the inlet velocity. In this work, an original segmentation-free superresolution (SR) solution is proposed using an inverse problem resolution approach by the minimization of a compound criterion involving three terms, a mechanical term based on Navier-Stokes equations, and a velocity smoothness promoting term, and a spatially weighted data fidelity term. The proposed solution has been validated regarding estimation error and computation time on simulated data and experimental acquisition from a phantom. Super-resolved velocity reconstruction demonstrates promising performance, even without segmentation knowledge, compared to state-of-the-art solutions.