Blood flow observation is of high interest in cardiovascular disease diagnosis and assessment. For this purpose, 2D Phase-Contrast MRI is widely used in the clinical routine. 4D flow MRI sequences, which dynamically image the anatomic shape and velocity vectors within a region of interest, are promising but rarely used due to their low resolution and signal-to-noise ratio (SNR). Computational fluid dynamics (CFD) simulation is considered as a reference solution for resolution enhancement. However, its precision relies on image segmentation and a clinical expertise for the definition of the vessel borders. The main contribution of this paper is a Segmentation-Free Super-Resolution (SFSR) algorithm. Based on inverse problem methodology, SFSR relies on minimizing a compound criterion involving: a data fidelity term, a fluid mechanics term, and a spatial velocity smoothing term. The proposed algorithm is evaluated with respect to state-of-theart solutions, in terms of quantification error and computation time, on a synthetic 3D dataset with several noise levels, resulting in a 59% RMSE improvement and factor 2 super-resolution with a noise standard deviation of 5% of the Venc. Finally, its performance is demonstrated, with a scale factor of 2 and 3, on a pulsed flow phantom dataset with more complex patterns. The application on in-vivo were achievable within the 10 min. computation time.