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## Main Question or Discussion Point

Hi,

Is there a method to represent a known two-dimensional vector field

$$ \vec{w}(x,y) = a \nabla b \, , \hspace{4mm} \nabla \cdot \vec{w} = 0 \, , \hspace{4mm} \nabla \times \vec{w} = f(x,y) \, ?$$

How would one proceed to calculate

Is there a method to represent a known two-dimensional vector field

**w**of two coordinates*x*and*y*with zero divergence and non-zero curl as$$ \vec{w}(x,y) = a \nabla b \, , \hspace{4mm} \nabla \cdot \vec{w} = 0 \, , \hspace{4mm} \nabla \times \vec{w} = f(x,y) \, ?$$

How would one proceed to calculate

*a*and*b*?