That's not Ohm's Law, that is a trait of constant wattage devices like induction motors driving a constant torque load, IE a compressor or conveyor belt, and SMPS (switched mode power supply) loads. For a compressor when you reduce the voltage the amps do go up until you hit a point where the motor can no longer supply the required torque and it stalls, at which point the amps go up to the locked rotor number till the overload device trips.
For fans and blowers motor power is to the square of the RPM and torque is directly proportional to airflow so with the right style of induction motor if you reduce the voltage you reduce the speed also, this is how the speed taps on a PSC blower motor work, the high tap is the lowest voltage tap of an autotransformer built into the run winding, the low speed is the highest voltage tap, the autotransformer function just intentionally undervolts the motor to make it run slower under load. With no load a PSC fan motor will turn the same speed on all speed taps. Try it some time, with the motor on high measure the voltage from the low tap to neutral.
Note that there are also true 2 speed induction motors for belt drive blowers that start and run as a 4 pole for high but start on 4 pole and switch to 6 pole for low.
IOW a 230v PSC CFM or IDB motor will run on 115 volts, it will just turn slower. A 230V compressor may start on 115v but will stall as soon as pressure starts to build up.