Assuming a geometric directional derivative remains controlled, smooth approximations converge to Yudovich-type weak solutions of the 2D density-dependent Euler equations, and such solutions are unique.
Fourier analysis and nonlinear partial differential equa- tions
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Yudovich theory under geometric regularity for density-dependent incompressible fluids
Assuming a geometric directional derivative remains controlled, smooth approximations converge to Yudovich-type weak solutions of the 2D density-dependent Euler equations, and such solutions are unique.