# Quiver in certain region - pgfplot

I am a novice to pgfplot, but got some web examples to create my own vectorized images. Since my specific problem has a vector field just at the upper region of the plane, I would like to draw just this part. For those who think "just plot the upper side of the axis", I have already thought it and, no, that is no acceptable answer. The goal is to plot more complex regions to make a domain with multiple different vector fields. The code is below. The exact region are separated by the curve on this plot:

\begin{tikzpicture}
\begin{axis}[
axis equal,
title={$u = 1$},
domain=-2:2,
view={0}{90},
axis background/.style={fill=white},
]
quiver={
u={y},
v={-x + 1},
scale arrows=0.1,
domain=0:2
},
-stealth,samples=15]
{0.5*((x - 1)^2 + y^2)};
\end{axis}
\end{tikzpicture}


I thank for the help and await anxiously. The proper region delimited by a line that separates the two fields I would like to draw is below.

Best regards.

pgfplots is based on TikZ, which allows you to clip.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis equal,
title={$u = 1$},
domain=-2:2,
view={0}{90},
axis background/.style={fill=white},
]
\clip (-2.5,0,0) -- (-1,0,0) arc (180:360:0.5)
arc (180:0:0.5) -- (2.5,0,0) -- (2.5,2.5,0) -| cycle;