Resolution of 1-foliations singularities on surfaces and threefolds

We consider resolution of singularities for 1-foliations on varieties of dimension at most three in positive characteristic. We prove that such singularities can be completely resolved if we allow tame regular Deligne--Mumford stacks as underlying spaces. If one restricts to underlying varieties, we show that 1-foliations singularities can be simplified into multiplicative ones.