B737-800
Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Multiengine; Flight Crew Instrument
Flight Crew Last 90 Days 214; Flight Crew Total 6346; Flight Crew Type 308
Aircraft Equipment Problem Less Severe
Flight Crew Landed As Precaution; Flight Crew Returned To Departure Airport
Aircraft
While on climb out at MDSD on RWY HDG from RWY 17 in day VMC; and passing 1;800 ft MSL for 3;000 ft MSL during clean-up from Flaps 1 to Flaps Up at 219 KIAS; the Capt's PFD (Primary Flight Display) displayed red tape over the airspeed (above and below the depicted airspeed); the airspeed was rapidly fluctuating and the Capt's stickshaker was in and out of activation.  My instruments and indications were all normal and cross-checked off of the standby instruments.As soon as the Capt's stickshaker activated; he verbally announced to me 'airspeed unreliable'; in which I immediately cross-checked my AOA (Angle of Attack) indicator; and my flight instruments to the standby instruments.  After I told him the aircraft was in a normal flight regime; I finished the 'After Takeoff' checklist with no abnormalities noted.  The Capt then called for the 'Airspeed Unreliable' checklist from the QRH.I ran the 'Airspeed Unreliable' checklist as the Capt maintained precise aircraft control while in and out of stickshaker.  After we finished the checklist determining that the airspeed was reliable on the FO's (First Officer) side and the standby airspeed indicator; we told Santo Domingo Approach that we had an aircraft instrumentation malfunction and we'd like to return to the airport  The Capt transferred aircraft control to me and made a call to the #1 FA (Flight Attendant).We ran the 'Descent'; 'Approach'; and 'Landing' Checklists in quick succession prior to being established on final.  I executed a raw-data visual approach to RWY 17 and made a Flaps 30/Autobrakes 3 heavy weight landing; approximately 15;000 lbs. overweight.  I touched down smoothly and softly on-speed; in the zone; with normal TR (Thrust Reverser) activation and braking upon landing roll-out.  During configuration to land; the Capt's stickshaker activated at least once prior to being established on final approach.We taxied the aircraft clear of RWY 17 to hardstand without incident and accomplished the 'After Landing' and 'Shutdown' checklists normally.
B737-800 First Officer reported the Captain's airspeed indicator malfunctioned shortly after takeoff. Flight returned to departure airport.