I live in the Mid-Atlantic US, in a region where lesser celandine (Ficaria verna) is highly invasive. It emerges in winter and often forms large monocultures, then flowers and dies before summer. The areas where it dominates are usually wet, bottomland areas with kind of fine, muddy, clayey soils. I have had it come up in my garden several places I've lived, as well as the gardens and yards of a number of people I have worked for, and it's usually been one of the toughest if not the single toughest plant for me to remove.
I haven't had the best luck trying to control it mechanically. It is so small, and it's covered in small bulblets, which both break off from aboveground stems, and below ground when I try to pull it, so, unless an isolated, individual plant comes up here or there, I have seen little benefit to attempts to dig it out, it seems to come right back the next year. I have tried cutting or mowing it, which seems to weaken it, but it seems a lot of work for relatively little benefit: it still comes back.
I am usually reluctant to use herbicide but I am open to suggestions of how to use herbicide safely and effectively, especially ones that are safe to apply near water as most of the areas where this plant is growing are near water.
I also am open to suggestions of native plants that might compete with it, or anything I can do to keep it from getting established on a site in the first place.
I also am curious if I'm missing anything system-level that might inhibit it, anything from leaf-litter to drainage and/or flooding. I am wondering if there are maybe things we've done to alter the drainage and/or soil texture that are perhaps favoring it, and if we could change how we interact with or manage the land, we could make it a bit less vigorous or less dominant.