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We consider a particle diffusing in the y-direction, dy/dt=\eta(t), subjectto a transverse shear flow in the x-direction, dx/dt=f(y), where x \ge 0 andx=0 is an absorbing boundary. We treat the class of models defined by f(y) =\pm v_{\pm}(\pm y)^\alpha where the upper (lower) sign refers to y>0 (y<0). Weshow that the particle survives with probability Q(t) \sim t^{-\theta} with\theta = 1/4, independent of \alpha, if v_{+}=v_{-}. If v_{+} \ne v_{-},however, we show that \theta depends on both \alpha and the ratio v_{+}/v_{-},and we determine this dependence.Comment: 4 page

Survival of a diffusing particle in a transverse shear flow: a first-passage problem with continuously varying persistence exponent