In this paper we propose an energy based algorithm for motion compensated video super-resolution (VSR) targeted on upscaling of standard definition (SD) video to high definition (HD) video. Since the motion (flow field) of the image sequence is generally unknown, we introduce a formulation for the joint estimation of a super-resolution sequence and its flow field. Via the calculus of variations, this leads to a coupled system of partial differential equations for image sequence and motion estimation. We solve a simplified form of this system and as a by-product we indeed provide a motion field for super-resolved sequences. Computing super-resolved flows has to our knowledge not been done before. Most advanced super-resolution (SR) methods found in literature cannot be applied to general video with arbitrary scene content and/or arbitrary optical flows, as it is possible with our simultaneous VSR method. Series of experiments show that our method outperforms other VSR methods when dealing with general video input and that it continues to provide good results even for large scaling factors, up to 8×8.