To improve the transmission performance of low Earth orbit (LEO) satellites limited by practical constraints of transmit power, antenna array size, and antenna gain in single satellites, multiple LEO satellites can be leveraged to cooperatively serve terrestrial user terminals (UTs). This paper investigates cooperative downlink (DL) transmission from multiple LEO satellites by using distributed beamforming, considering the inevitable delay and Doppler compensation errors that impact coherent processing. Firstly, we establish the DL transmission signal model for multiple LEO satellites with delay and Doppler compensation errors. On this basis, we design the transmitters and receivers to maximize the average signal-to-leakage-plus-noise ratio. Then, we analyze the DL transmission performance via deriving lower bounds and closed-form expressions for both the user rate and the average rate gain of cooperative transmission compared to single LEO satellite transmission. We prove that as the number of receiving antennas at the UT increases, the impact of imperfect compensation on the user rate decreases, and the average rate gain improves. In addition, we prove that the UT can achieve the optimal average rate gain when its array response vectors corresponding to different LEO satellites are orthogonal. Simulations are performed and compared to the theoretical analysis, demonstrating the performance gains brought by distributed beamforming and validating our analysis.