On local smooth solutions for the Vlasov equation with the potential of interactions<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\pm r^{-2}$"><mml:mo>±</mml:mo><mml:msup><mml:mi>r</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>
International journal of mathematics and mathematical sciences