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Dec 7, 2016 at 16:54 comment added 0xbadf00d Please take note of my last three comments below the question. I'm only interested in mild solutions of $(2)$; which should be easier than finding a weak solution. From my understanding, $(3)$ is the wrong equation to consider, unless one is searching for weak solutions. However, I can't find any good reference which is considering mild solutions of $(2)$ (and hence of $(6)$).
Dec 7, 2016 at 16:49 history answered Jean Duchon CC BY-SA 3.0