Euler's Master's Thesis
Martin Mattmüller, in his article Leonhard Euler, seine Heimatstadt und ihre Universität on Euler's hometown Basel, writes that this public talk (not a dissertation or written thesis), which Euler gave in 1724, is lost, and that it is not known which position he supported. Euler had obtained his magister degree already in 1723.
As Franz says, it is impossible to know for definite which view the young Euler supported.
However, Newton had already disposed of the Cartesian vortex theory in the Principia which was published almost $40$ years before. I presume that Euler must have supported the view of Newton as Euler had almost certainly read the Principia by that age. I don't know how the history goes though, or how long it took for certain people to accept that the model of Descartes was definitely incorrect.
I suspect that at first there might have been quite a lot of resistance to Newton's views, but if the view of Descartes was still regarded as a tenable one in 1724, that is very interesting to me.