WDB ACFT HAS DIMINISHING TIRE PRESSURE OF 1 MAIN GEAR TIRE.

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ON AN AUGMENTED CREW FLT AT THE CREW CHANGE OVER POINT (1/2 WAY ENRTE) I WAS INFORMED BY THE RELIEVED CREW THAT THE #14 MAIN GEAR TIRE PSI WAS GOING DOWN. THE PSI FOR THAT TIRE AND THE #13 TIRE ON THE GEAR SYNOPTIC INDICATED 'AMBER.' THE #13 TIRE PSI SHOWED NORMAL AT 205 PSI. #14 SHOWED 100 PSI. I CONTACTED OUR COMPANY MAINT CTL AND DISCUSSED THE PROB. WE DECIDED TO LAND ON THE LONG RWY AT JFK (31L) AND REQUESTED THE EMER TRUCKS TO STANDBY. WE ALSO REQUESTED THE COMPANY TO HAVE MECHS AVAILABLE TO CHK US OVER AFTER RWY TURNOFF. I ALERTED THE LEAD FLT ATTENDANT EARLY ON AND INSTRUCTED HER TO PREPARE THE CABIN AND OTHER FLT ATTENDANT'S FOR POSSIBLE PROBS ON THE ROLLOUT. THE LNDG WAS NORMAL AND AFTER WE CLRED THE RWY WE STOPPED THE ACFT. THE MECHS PINNED THE GEAR (ALL GEAR) AND CHKED US OVER. THE MECHS CALLED ON THE INTERPHONE AND TOLD US THAT THE #14 TIRE WAS INDEED FLAT BUT THE TIRE AND GEAR WERE INTACT WITH NO DAMAGE NOTED. WE TAXIED IN TO OUR GATE WITH NO OTHER PROBS. THIS INCIDENT SHOWED ME THAT IF THE COMPLETE CREW WORKS TOGETHER AND EVERYBODY DOES HIS OR HER JOB; THINGS USUALLY GO GOOD. EVERYTHING WORKED WELL AND SAFETY WAS PARAMOUNT IN ALL OUR MINDS. EVEN THOUGH WE WERE TIRED (14 HR FLT) ALL THE CREW HAD SOME INPUT AND THE FLT WAS SAFELY COMPLETED.