Recently, several experiments on La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) challenged the Fermi liquid picture for overdoped cuprates, and stimulated intensive debates [1]. In this work, we study the magnetotransport phenomena in such systems based on the Fermi liquid assumption. The Hall coefficient $R_H$ and magnetoresistivity $rho_{xx}$ are investigated near the van Hove singularity $x_{tinytext{VHS}}approx0.2$ across which the Fermi surface topology changes from hole- to electron-like. Our main findings are: (1) $R_H$ depends on the magnetic field $B$ and drops from positive to negative values with increasing $B$ in the doping regime $x_{tinytext{VHS}}<xlesssim0.3$; (2) $rho_{xx}$ grows up as $B^2$ at small $B$ and saturates at large $B$, while in the transition regime a nearly linear behavior shows up. Our results can be further tested by future magnetotransport experiments in the overdoped LSCO.
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