Currents in a few-electron parabolic quantum dot placed into a perpendicular magnetic field are considered. We show that traditional ways of investigating the Wigner crystallization by studying the charge density correlation function can be supplemented by the examination of the density-current correlator. However, care must be exercised when constructing the correct projection of the multi-dimensional wave function space. The interplay between the magnetic field and Euler-liquid-like behavior of the electron liquid gives rise to persistent and local currents in quantum dots. We demonstrate these phenomena by collating a quasi-classical theory valid in high magnetic fields and an exact numerical solution of the many-body problem.
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