Detection of the electromagnetic emission from coalescing binary neutron stars (BNS) is important for understanding the merger and afterglow. We present a search for a radio counterpart to the gravitational-wave source GW190425, a BNS merger, using Apertif on the Westerbork Synthesis Radio Telescope (WSRT). We observe a field of high probability in the associated localisation region for 3 epochs at 68, 90 and 109 days post merger. We identify all sources that exhibit flux variations consistent with the expected afterglow emission of GW190425. We also look for possible transients. These are sources which are only present in one epoch. In addition, we quantify our ability to search for radio afterglows in fourth and future observing runs of the gravitational-wave detector network using Monte Carlo simulations. We found 25 afterglow candidates based on their variability. None of these could be associated with a possible host galaxy at the luminosity distance of GW190425. We also found 55 transient afterglow candidates that were only detected in one epoch. All turned out to be image artefacts. In the fourth observing run, we predict that up to three afterglows will be detectable by Apertif. While we did not find a source related to the afterglow emission of GW190425, the search validates our methods for future searches of radio afterglows.
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