electronic speed control

Hello

Does all ESCs work with all brushless motors? Or does each motor have a specific set of ESCs? I am looking for an ESC for DC 1.5-4.5V 50000RPM 1mm Dia Shaft Coreless Motor for RC Helicopter.

Thanks

No, each ESC is designed for a particular range of currents and voltages.

For a coreless motor you don't need an ESC, its not a brushless motor.