In the core-accretion model the nominal runaway gas-accretion phase brings most planets to multiple Jupiter masses. However, known giant planets are predominantly Jupiter-mass bodies. Obtaining longer timescales for gas accretion may require using realistic equations of states, or accounting for the dynamics of the circumplanetary disk (CPD) in low-viscosity regime, or both. Here we explore the second way using global, three-dimensional isothermal hydrodynamical simulations with 8 levels of nested grids around the planet. In our simulations the vertical inflow from the circumstellar disk (CSD) to the CPD determines the shape of the CPD and its accretion rate. Even without prescribed viscosity Jupiter's mass-doubling time is $∼ 10^4$ years, assuming the planet at 5.2 AU and a Minimum Mass Solar Nebula. However, we show that this high accretion rate is due to resolution-dependent numerical viscosity. Furthermore, we consider the scenario of a layered CSD, viscous only in its surface layer, and an inviscid CPD. We identify two planet-accretion mechanisms that are independent of the viscosity in the CPD: (i) the polar inflow -- defined as a part of the vertical inflow with a centrifugal radius smaller than 2 Jupiter-radii and (ii) the torque exerted by the star on the CPD. In the limit of zero effective viscosity, these two mechanisms would produce an accretion rate 40 times smaller than in the simulation. ; Comment: 11 pages, 10 figures. Accepted for publication in Astrophysical Journal