Paolini’s match against Pliskova lasted just six minutes.

Sinner speaks:

He’s a tough opponent, we played each other in Cincinnati, so I knew what to expect. I always love New York, it’s a very special place, every match is different, has its own story, so I’m very happy.

It has to be said Sinner had a lot of support from the crowd during the match, despite facing an American and despite the scrutiny he’s faced over the past week. He’ll be relieved to come through so comfortably after his tough opener on Tuesday.

Sinner beats Michelsen 6-4, 6-0, 6-2

Thompson beats seventh seed Hurkacz

Sad scenes on Louis Armstrong, where Karolina Pliskova, the 2016 finalist and former world No 1, is hobbling off, having retired in the first game against Jasmine Paolini, the French Open and Wimbledon runner-up. Paolini will play Putintseva next.

What of Boulter, you say? Well since she traded breaks with Bouzas Maneiro, it’s been going with serve, but the British No 1 is in danger serving at 5-5, 30-all, and the alarm bells are then ringing at 30-40. Bouzas Maneiro seizes the break with a forehand winner – and then serves out the set to love. “Horrendous, horrendous,” Boulter said to her coach at one point. I don’t think it’s been horrendous – but after starting so strongly, but failing to secure the scoreline her early play deserved, she’s looked rather edgy and needs to regather her composure in the second set.

Sinner has served a New York bagel (surely the best kind) to Michelsen, and now leads 6-4, 6-0.

Also through: The Italian 30th seed Matteo Arnaldi, who’ll next face either Thompson or Hurkacz, who’s still digging deep, locked at 5-all in the third set, with Thompson leading 7-6 (2), 6-1.

Another result: Yulia Putintseva has claimed her first win in four attempts against Wang Xinyu, coming through a much harder second set to advance 6-1, 7-6 (4).

Tomas Machac won’t be too popular on Louis Armstrong, because the Czech has defeated the home hope and 16th seed Sebastian Korda in three impressive sets, 6-4, 6-2, 6-4. Korda had such a strong build-up to the US Open, winning the title in Washington and reaching the Canadian Open semis, but he goes no further than the second round here.

Hurkacz, despite the knee injury he suffered at Wimbledon and the calf problem he picked up in Cincinnati, is doing his best to force a fourth set against Thompson, and he’s got the crowd whooping and hollering after this point too.

Sinner has hit his stride. After struggling to pull away from Michelsen in the first set, he’s in command in the second, leading 6-4, 4-0.

But then out of nowhere Boulter is broken straight back, as her first serve deserts her, and she throws in a double fault too. She’ll be kicking herself, having looked so comfortable up until this point. It’s now 4-3 Boulter.

Boulter is rewarded for her endeavour. 3-2 up, she has two break points at 15-40. There are just too many unforced errors from her opponent at the moment. And here’s another, as Bouzas Maneiro blazes a backhand wide! Boulter is 4-2 ahead, a different story to her first-round match when she had to come from a set down, having had a very limited build-up to the US Open because of her participation at the Olympics.

Boulter is under way on Court Five. The British No 1, who’s seeded at the US Open for the first time, is up against Spain’s Jessica Bouzas Maneiro, world ranked 74 but not to be taken lightly, having defeated the defending champion Marketa Vondrousova in the Wimbledon first round this summer. Boulter has done the early pushing and probing but her efforts are yet to be rewarded with a break; she leads 3-2 on serve.

Sinner has claimed what could prove to be a decisive break in the first set. The top seed now leads Michelsen 5-4. But he’ll now have to do something he’s not managed during this match so far, and that’s hold serve after breaking. Again it’s not the most assured of service games, but from 30-all he advances to set point at 40-30, and off a second serve secures the set 6-4 when Michelsen can’t direct his return back into play.

A second result of the day: Diana Shnaider, the Russian or rather neutral flag player, has beaten Denmark’s Clara Tauson, 6-4, 6-4. The 18th seed, who won Olympic silver in the women’s doubles alongside Mirra Andreeva, will face the winner of the match that now follows on Court Seven between the Italian veteran Sara Errani and the American Caroline Dolehide.

Korda’s had treatment on his right arm, which is covered in a black sleeve today, and the timeout has done the trick, because he’s 3-0 up in the third against Machac. But he’s got plenty of work still to do, trailing by two sets to love, 6-4, 6-2. Thompson, meanwhile, now has a two-sets lead, 7-6, 6-1 against an ailing Hurkacz.

Sinner strikes for 4-3. But just like after he broke in the opening game, he’s immediately under pressure on serve at 0-30. Then 30-40, after an improvised crouching return from Michelsen helps set up a break point for the energetic American. Deuce, then another break point at Michelsen’s advantage. And Sinner biffs a backhand into the net and they’re all square once more! It’s 4-4.

Machac, rocking some very short shorts, is now two sets to the good against Sebastian Korda, 6-4, 6-2. And after those two opening breaks, Sinner v Michelsen has settled into a serving rhythm, with the pair level at 3-3.

Anna Kalinskaya is the first player of the day to put a W by their name. The 15th seed, who’s playing as a neutral athlete here, like her fellow Russians, has defeated Hungary’s Anna Bondar 6-2, 6-4, serving it out to love. The result means that it’ll be Brits all the way on Court Five from here on in, with Katie Boulter up first, followed by Jack Draper and then Dan Evans.

Hurkacz is throwing his racket around on Court 17 after missing by a mile. The seventh seed has not won a game in the second set and trails Thompson 7-6, 3-0.

Michelsen, I should have said, gave Sinner a scare at Cincinnati this month and the 20-year-old is relishing the chance to test the Italian with a home crowd behind him. “I’m going to go out there and I’m going to compete my hardest,” Michelsen said before the match. “I’m going to be the underdog and I love being the underdog so it’ll be fun either way.”

Jannik Sinner is under way on Arthur Ashe, and the world No 1 has broken the young American Alex Michelsen in the opening game, in sharp contrast to his slow and uncertain start in round one, when he trailed by a set and a break. Jim Courier is asked on Sky Sports how much Sinner’s positive drugs tests may have affected him in that opening match. “We’re just speculating but by looking at the first set and a half he looked like he needed to get his feet underneath him,” Courier says, just as Sinner is stung by an immediate break back by Michelsen.

Tomas Machac is another player who’s turned things around. From 4-2 down in the opening set against Sebastian Korda, he’s now 6-4, 2-1 ahead, so has won six of the past seven games against the American.

They’re into a tie-break on Court 17. And Hurkacz does love a tie-break. It’s his 50th of the year. But Thompson, with arm sleeves on both arms and a neon yellow cap as bright as the balls, is now proving irrepressible. The Aussie, having trailed 4-1 in the set, brings up four set points at 6-2 and Hurkacz gives it away with a double fault!

Kalinskaya’s being made to work a bit harder by Bondar in set two. The longest rally of the match, 17 shots, and Kalinskaya is taken to deuce. Make that break point. For the first time today the 15th seed is looking a little anxious. She flumps a forehand into the net and Bondar breaks back for 2-2 in the second set. Meanwhile Yulia Putintseva has the first set in the bag, 6-1, against Wang Xinyu.

Hurkacz is serving for the first set at 5-3 but Thompson has other ideas. The Australian, who at the age of 30 is playing some of the best tennis of his career, carves out two break points at 15-40 and then, on the back foot and on the run, produces a passing winner to break back! Two holds follow so Thompson will serve at 6-5 down to force a tie-break.

There were also some strong – and important – words from Caroline Garcia yesterday about the damaging abuse players are receiving on social media when they lose and how “unhealthy betting” is fuelling the hate. It was good to see Garcia receiving support from the locker room, including Iga Swiatek and Madison Keys, who both thanked her for speaking up. The American Jessica Pegula – somewhat depressingly – said: “The constant death threats and family threats are normal now, win or lose.”

If you missed any of yesterday’s results, by the way, you can catch up here:

Tomas Machac has broken back against Sebastian Korda. The Czech is now serving at 4-3 down. And the first set of the day has – unsurprisingly – gone to Anna Kalinskaya, 6-2 against Anna Bondar.

Hubie Hurkacz isn’t messing around either. The Pole, who injured his knee diving for a ball during his second-round loss at Wimbledon, has done something of a Djokovic by returning from surgery so quickly, and he’s 5-2 up here against Jordan Thompson, who’s being watched by the Australian Davis Cup captain Lleyton Hewitt. Hurkacz did face a break-back point in the previous game – but reeled off the next three points to hold.

It’s been a flying start, meanwhile, from Sinner’s girlfriend, Anna Kalinskaya, who could be a player to watch this fortnight. She’s in a fairly favourable section of the draw, but in the fourth round may meet Elena Rybakina, who beat her at the same stage at Wimbledon last month. Kalinskaya leads Hungary’s Anna Bondar 5-1 – and with that match taking place on Court Five, it could mean Britain’s Katie Boulter is in action sooner than expected. Kalinskaya is playing doubles here with Boulter, by the way.

I must admit I’ve not watched much of the tournament so far, as I was covering the Paralympics opening ceremony last night and was en vacances in France before that, so I’m looking forward to getting stuck into the tennis today, especially having a look at what kind of physical and mental shape Jannik Sinner is in after his positive drugs tests became public.

The players have made their way to their respective courts at Flushing Meadows, they’ve finished their warm-ups, and here are the early runners and riders: Sebastian Korda, the 16th seed and son of the 1998 Australian Open champ Petr, is up against the Czech Tomas Machac, who won Olympic mixed doubles gold in Paris; Yulia Putintseva, the 30th seed, is taking on China’s Wang Xinyu; it’s the battle of the two Annas between Kalinskaya, the 15th seed, and Bondar; while on Court 17 it’s Jordan Thompson, one of six Australian men in singles action today, against the Polish 7th seed Hubert Hurkacz.

Order of play (selected courts)

Tim Henman is on Sky Sports and says he’s been speaking to Dan Evans. Apparently Evans is in better shape than expected after his marathon on Tuesday, and spent yesterday having an ice bath, massage and doing some work on a stationary bike to relieve his achy legs.

The Brit is scheduled fourth on Court Five today, so at least that gives him a bit more recovery time. And he’ll be relieved that the extreme heat of yesterday has given way to much more player-friendly conditions, with a high of 25 degrees forecast. Frances Tiafoe said he brought 20 shirts and three pairs of shoes on to the court yesterday because he was sweating so much; I don’t think such drastic measures will be needed by anyone today.

Preamble