I want to plot a piecewise-smooth vector field. For instance:
$F_1(x,y) = (x^2 + y^2, y^2)$, $F_2 (x,y) = (2xy,2xy-x^2)$ and $H(x,y) = x-y$
$F(x,y) = \begin{cases} F_1(x,y) \text{ if } H(x,y) >0 \\ F_2(x,y) \text{ if } H(x,y)<0 \end{cases}$
How can I plot $F(x,y)$ in Mathematica?
Piecewise
+VectorPlot
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