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That's about it for our live text updates for today - let's do it all again tomorrow, shall we?

On Wednesday, British number one Emma Raducanu will be first on Louis Armstrong Stadium.

Her second-round match against Indonesian qualifier Janice Tjen is scheduled to start at 16:00 BST and you'll be able to follow that live here on the BBC Sport website and app.

The only other British player in action on Wednesday is Cameron Norrie, who is second on Court 5 against Argentina's Francisco Comesana.

We've also got Novak Djokovic, Jessica Pegula and plenty of other stars aiming for spots in round three.

Hope you can join us then.

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• British duo Katie Boulter and Sonay Kartal were beaten by seeds in their first-round matches at Flushing Meadows. Boulter lost in straight sets to Marta Kostyuk, while Beatriz Haddad Maia got past Kartal in a decider.
• Fellow British player Fran Jones, who came through qualifying to reach the main draw, lost to Eva Lys in straight sets.
• Wimbledon champion Iga Swiatek needed just 60 minutes to beat Colombia's Emiliana Arango 6-1 6-2.
• Amanda Anisimova - the player Swiatek beat in last month's final at SW19 - beat Kimberly Birrell 6-3 6-2.
• Former US Open champions Naomi Osaka and Coco Gauff are in first-round action in Tuesday's evening session.

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• World number one and defending champion Jannik Sinner raced to a straight-set win over Vit Kopriva, dropping only four games en route to round two.
• Tenth seed Lorenzo Musetti recovered from a set down against Giovanni Mpetshi Perricard to win 6-7 (3-7) 6-3 6-4 6-4 and book his place in the second round.
• Things were more straight forward for 27th seed Denis Shapovalov, who took just over two hours to win in straight sets 6-4 6-4 6-0 against Marton Fucsovics.
• Francisco Cerundolo did it the hard way against Matteo Arnaldi, the 19th seed coming from two sets down to win 3-6 2-6 7-5 6-4 6-3.
• Alexander Bublik took less than two hours to beat former US Open champion Marin Cilic, the 23rd seed winning in straight sets.

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Felix Auger-Aliassime, speaking on court after his win over Billy Harris: "What an atmosphere! I felt it, especially after a couple of years without a win here. The atmosphere was electric so thank you guys.

"It is a good win for me. I'm pleased to have got it done in three sets because he [Billy Harris] is a tough opponent. He has been getting better every year and he is a player with a lot of strengths, so it was a good first-round win for me.

"The crowd definitely played a role in the win. They were kind of playing with both of our emotions out on court. That's what you play for as a player, so I hope their energy lasts for the whole tournament."

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British number three Sonay Kartal spoke to BBC Radio 5 Live following her first-round defeat by 18th seed Beatriz Haddad Maia: "My tennis in the last couple of weeks hasn't been anywhere near what I would like it to be. My level is just a little bit off at the minute so the first set was a little bit nervy. I was just trying to play my way in, create more opportunities and be patient.

"I knew I had to change some things in the second set and be more aggressive, that's what I've been doing when I've been more successful over the past few months. I was trying to dial into that and it was working. I was feeling good on the ball and she almost didn't really know what to do.

"In the last game of the second set, I knew something was a little bit off. I've never fully cramped, my equivalent to that is my muscle spasming and then releasing pretty fast. I was getting a bit of that so I was just trying to talk to my team at the end of the second set, which is why I took the bathroom break to see if there was anything I could do.

"I wasn't expecting everything to fully go at the start of the third set though. There was something different locking up all the time. At one point, my thumb was wrapped around my racquet and I couldn't release it in time to hit the next ball. It was definitely a new experience.

"I think there was something I was probably missing, like my salt intake or something like that, I don't think it was anything physically. I'll have to look over the last few days and make some changes."

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Four defeats out of four for British players today.

There's still one more Briton waiting to start his first-round match and it'll be a little while before Jacob Fearnley gets on court against world number 47 Roberto Bautista Agut.

That was a cracking match - Felix Auger-Aliassime wins in straight sets but it felt much closer.

World number 151 Billy Harris will rue those three missed set points in the second set but can be proud of how he played, pushing the former top 10 player all the way.

Ken Skupski
Former British player on BBC Radio 5 Sports Extra and BBC Sounds

Billy Harris is still alive! That was a great return down the line, I actually thought Felix Auger-Aliassime wasn't going to get that back but then the Brit had to hit another couple of shots. He did really well there.

Both players are coming up with some terrific shot-making.

Felix Auger-Aliassime gets to the net, and sets himself for a between-the-legs volley but there's no need to execute it as Harris nets, and the Canadian has a break point.

And he has his break when Billy Harris double-faults for just the second time in the match.

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Ken Skupski
Former British player on BBC Radio 5 Sports Extra and BBC Sounds

Felix Auger-Aliassime is giving away some really cheap points.

He had the opportunity there to close this game out and maybe go on to serve for the match. His backhands just keep sailing long.

When Auger-Aliassime does get ahead in games, I feel he is a little bit more dynamic with his movement than Billy Harris.

Both players are performing well now, and the crowd are really getting into the match.

"Let's go, Billy, let's go!" is the chant from the British contingent.

But Felix Auger-Aliassime manages to hold.

There hasn't been much for British fans to cheer about today but Billy Harris is really putting up a fight.

He holds with a service winner, clenching his fist as he jogs back to his chair.

Auger-Aliassime begins his service game with an ace but Billy Harris isn't done yet.

He whips a forehand winner cross-court, before a forehand unforced error from the Canadian gives the Briton two break points.

Auger-Aliassime saves both with two big serves but he can't save a third, which Harris wins at the net.

We're back on serve!

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Uh-oh, this is trouble for Billy Harris, as Felix Auger-Aliassime breaks him to love, finishing the game with a couple of confident winners.

That's eight points in a row for the Canadian, who is now a break up in the third set.

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A love service game from Felix Auger-Aliassime and the pressure is back on Billy Harris.

Here's trouble for Billy Harris, who slips to 0-30 on his serve but extricates himself from danger with some good serving and edges ahead in the set.

Harris hasn't given up - nor have a group of fans who are noisily encouraging the Briton as he sits down at that change of ends.

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Felix Auger-Aliassime holds serve. Snaffling that set will have given him confidence that he can finish this in three.

Urged on from courtside by his dad Geoff, Billy Harris starts the third set by holding serve.

That's a good response from the Briton, who must have been devastated to see that second set slip through his fingers.

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Billy Harris has gone off court, presumably to try to regroup after that second set - but that will be a tough one to take after missing those three set points, one of which came on his own serve.

Harris has never played a Grand Slam five-set match but that's what he'll have to do if he wants to stay in this tournament.