A319 flight crew reported an engine malfunctioned at cruise; then recovered; and re-occurred again during the descent. The flight landed safely and a write up was sent to maintenance.

Narrative

In cruise at FL350 the first indication I noticed of an abnormal was the aircraft rolling and yawing slightly left. Then I noticed that Engine 1's N1 was rolling back significantly from what was commanded. My first call was Engine Failure"; but this was not actually the case. The ECAM then displayed the message Eng1 Stall. With a priority toward flying the aircraft first we requested a lower altitude and started to access the situation. During this time the Engine recovered and the ECAM message cleared. With the ECAM message gone and the engine functioning normally again we looked to the QRH for further guidance. The main takeaway we found was that if the engine function returned to normal we could continue normal ops. At this point our thinking was to just keep monitoring and continue to ZZZ. We also turned on Engine Anti-Ice for extra bleed loading per the QRH guidance.During descent we experienced another re-occurrence of the number 1 engine's N1 rolling back. This time no ECAM message was presented. Now with the knowledge of the QRH procedure we planned to start that procedure. Again; moments later the engine function returned to normal. So again we put that procedure on hold.At this point it was clear to us the Engine was functioning; but it was not reliable. We opted to basically plan for an engine out approach. We started the APU; turned on Engine Ignition; and we planned a Flaps 3 landing. I opted to make the landing due to having more experience than the FO on the airplane. We briefed our intention to be completely setup for a single engine approach and execute one if needed.We coordinated all of this with ATC; dispatch; the flight attendants; and the passengers. We made an uneventful landing on RWYXXC; allowed Airport Rescue and Firefighting (ARFF) to inspect the engine out and follow us to the gate out of an abundance of caution.Maintenance was notified and an entry was made in the Logbook. Mechanical Issue with Engine 1.Honestly; I think we preformed excellent as a crew. Without knowing the root cause of the mechanical problem; I'm not sure what could have done better."