Australia's young quicks wilted in the oppressive Brisbane heat, another bowler was lost to injury and India's batsmen were well on top at the Gabba fortress. Welcome to the Australian captaincy, Steve Smith.

Through no real fault of his own, Smith endured a tough first day at the office as Test skipper, his team under physical duress and in trouble on day one of the second Test as Indian opener Murali Vijay continued his relentless runscoring against Australia.

Vijay unfurled a brilliant 144, his fourth century in eight matches against Australia. It was the second-highest score by a visiting opener at the Gabba, behind Alastair Cook's unbeaten double-century in 2010.

India were 4-311 at stumps, with the elegant Ajinkya Rahane unbeaten on 75, Rohit Sharma on 26 and more batting to come after the return of captain MS Dhoni and spinner Ravi Ashwin. It was the second-highest first-day score by a visiting team at the Gabba, where Australia has not lost a Test in Smith's lifetime.

Vijay has made 976 runs at an average of 69 against Australia and his reprieve on 36, when recalled batsman Shaun Marsh grassed a low catch at third slip, was a let-off the home side could ill afford.

Nor could the Australians afford a hamstring injury to young allrounder Mitchell Marsh, who grimaced and left the field after his sixth over shortly after celebrating his maiden Test wicket. His departure left Smith with a depleted attack as the temperature soared to the mid-30s but coach Darren Lehmann refused to use the heat as an excuse for India's cascade of runs in the last session.

Marsh's injury was only the beginning of the Australian bowlers' physical struggles.

Debutant Josh Hazlewood was the best of the bowlers, gaining steep bounce and a bit of swing, but fell on the pitch and had to be treated for cramp after collecting the wickets of Cheteshwar Pujara and Virat Kohli. Later, the 23-year-old couldn't complete his first over with the second new ball and had to leave the field with physiotherapist Alex Kountouris.

Hazlewood's most recent first-class game was in early November. "He had cramps all over his body, so it wasn't just one place," Kountouris said. "With him it was his calves, both hamstrings, groin, hips, he just couldn't function.

"You could see his pace was down when he came back to bowl and he showed some courage to do that because he really struggled. Every ball he bowled he was cramping up in multiple places."

Hazlewood is expected to bowl on day two.

Mitchell Starc had to leave the field in distress from the heat and returned only to clutch at his ribcage. In the Channel Nine commentary box Shane Warne was highly critical of Starc's body language, but Kountouris said he was struggling with rib and back pain. "We think he is going to be able to bowl tomorrow."

Even Mitchell Johnson, so destructive at the Gabba last summer and now, in the absence of Peter Siddle and Ryan Harris, the undisputed spearhead, was subdued. Both left-armers went for four runs an over.

With the exception of a couple of deliveries that reared up and were gloved to the vacant leg gully region, the Indian batsmen played him without too much trouble. Johnson was also bothered by a sore finger on his bowling hand, receiving a blow on a spot that he hurt during the previous Test series in the United Arab Emirates.

"He is generally sore but he is fine," Kountouris said.

Lehmann was critical of the bowling with the exception of the middle session, when Hazlewood struck twice.

"We didn't get it quite right for a long period of time, second session we certainly did, third session we were too full or too wide and we couldn't hit our lengths the whole time. It was very hot and we understand that as a group and a team but we've got to be better than that in the last session," he said.

"We went for 160 in 30 overs which is not what we're about."

Medical staff now face a huge challenge to nurse the bowlers through the match.

"The difficulty of today was it's day one. You probably cop this if it was day three or day four, it makes the next four days very, very long," Kountouris said.

Vijay, who brought up his century with a beautiful cover drive off Shane Watson and seemed too dazed by the heat to celebrate, was given another life on 102 when Shaun Marsh misjudged the pace of the ball at short cover.

He attacked Nathan Lyon, whose main asset on this pitch was bounce rather than turn.

Eventually the opening batsman charged the off-spinner and took a tired swipe, and was caught behind.

Smith had to turn to David Warner's medium pace and bowled an over of his own wrist spin before taking the second new ball. There was little else he could do in the circumstances, and his only real mistake was to lose the toss.

"I thought he coped really well considering the revolving door. In and out, we didn't know who was out on the field. We had [spin coach] John Davison  in his whites," Lehmann said.

Smith was also slow getting through the overs, with just 83 bowled for the day.

Vijay and Shikhar Dhawan got through the first hour, Dhawan tempering his attacking instincts. But the left-hander could control himself for only so long, and attempted to cut a short, wide ball from Marsh.

Cheteshwar Pujara paid the price for India's refusal to use the DRS, out for 18 when umpire Ian Gould ruled he was caught behind from a short-pitched delivery from Hazlewood.

Replays indicated the ball came off the grille of his helmet.

It was an unusual way for debutant Hazlewood to collect his first Test wicket, but there was no doubt about his second. The dangerous Kohli was fooled by the extra bounce when he attempted a cut shot and was caught behind for 19.