That's all from us but you can continue listening to BBC Radio 5 Live commentary by clicking the play icon at the top of this page.
If you need to catch up on the day's action so far, here's a reading list:
British teenager Emma Raducanu won on her US Open main-draw debut
Alexander Zverev hopes to 'challenge' Novak Djokovic after a composed opening win
Czech fourth seed Karolina Pliskova powered past American Catherine McNally to reach the US Open second round.
'I am exceptionally proud'
And here is Ash Barty: "I was disappointed not to be able to play last year but this year with fans has made it all the better, the city is buzzing and it is nice to share this with everyone here today.
"I am exceptionally proud, we made the right decisions for us - we trained and got ready, came into this year with the attitude it was going to be a different adventure for us, but it has been really enjoyable right from the start."
On hitting balls with golfer Ian Poulter: "I do love playing golf, it is a hobby of mine, I haven't played as much as I would have liked, I come from a golfing family so it is nice to hit a few balls."
Post update
Barty's second-round opponent was decided just as she wrapped up that victory.
She will face world number 78 Clara Tauson next. The Dane has just beaten France's Clara Burel 7-5 6-0.
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Naomi Broady
British player on BBC Radio 5 Live Sports Extra
She didn't look that happy, I wonder if sometimes you lose perspective as to how well your opponent is playing.
Vera Zvonareva loops her forehand long and world number one Ashleigh Barty is through to the second round.
The Russian put up some impressive resistance in that second set.
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Barty 6-1 6-6 Zvonareva*
Barty seemed to work out what shot to hit that time.
She comes in for a forehand volley and lightly taps it over the net to bring up her second match point.
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Naomi Broady
British player on BBC Radio 5 Live Sports Extra
She is just not affected by the slice at the moment, Zvonareva, she is staying patient and it is almost like Ash Barty doesn't know what shot to hit at the moment.
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Laura Robson
Former British number one on BBC Radio 5 Live Sports Extra
Ash Barty does not look happy with this situation...
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Barty 6-1 6-6 Zvonareva*
The crowd almost groans as Barty's forehand just stays inside the lines. Match point saved.
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Barty 6-1 6-6 Zvonareva*
Set point Zvonareva!
Barty's backhand goes long.
The Australian was so, so dominant. Now we could be going to a decider.
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Barty 6-1 6-6 Zvonareva*
It really felt like Barty was building through the lengthy rally, smelling blood. But no... her forehand goes into the net and we go on. 6-6.
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Barty 6-1 6-6 Zvonareva*
The Russian can't back it up as she is outpowered by Barty's forehand. 6-5 - match point to the Australian.
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Barty 6-1 6-6 Zvonareva*
Nope.
Zvonareva repays Barty for her earlier booming backhand down the line with one of her own and claws the break back. Back on serve at 5-5.
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Barty 6-1 6-6 Zvonareva*
A backhand into the net brings up 5-4 but if Barty can hold both her serves here she's into the second round.
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Barty 6-1 6-6 Zvonareva*
Lovely serving from Barty and her 11th ace of the match makes it 4-3.
The Australian's backhand winner down the line is perfect to go a mini-break up at 5-3.
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Laura Robson
Former British number one on BBC Radio 5 Live Sports Extra
How good was that spin from Ash Barty on the forehand side - she has such easy technique that it just makes it look like she was born this good.
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Barty 6-1 6-6 Zvonareva*
Break back secured. Zvonareva's shouts reach their highest pitch as she realises she's not got the measure of Barty in a lengthy rally.
Her forehand goes into the net and it's back on serve at 3-2.
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Barty 6-1 6-6 Zvonareva*
Zvonareva holds her first serve. Barty holds hers too, but then bats her forehand long to give the Russian an early break at 2-1 up.
Barty takes it to a tie-break
Barty 6-1 6-6 Zvonareva*
This is more like it.
All of a sudden Barty looks back to her best as she whips a forehand winner into the left corner for 40-15.
A serve out wide takes us to the tie-break.
Post update
*Barty 6-1 5-6 Zvonareva
Ashleigh Barty has hit 16 unforced errors in this second set.
The 16th brings up 0-15 but she pulls off an impressive forehand winner for 15-15.
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ESPN+ coverage includes all outer courts throughout the week. ESPN+ coverage began with the Qualifiers, and continues through the entirety of the tournament, including coverage of the Men's Singles Championship. 1 p.m. – 2 p.m.
On top of airing on ESPN, US Open matches will stream live on ESPN+, so if you don't want to pay for a pricey cable or streaming package that includes ESPN, this is a budget-friendly alternative.
The Open Radio channel is available on satellite channel 92 and streaming on the SiriusXM app. Championship broadcasts begin on Thursday and Friday at 2am ET and on Saturday and Sunday at 4am ET, continuing through the conclusion of each day's play.
ESPN is the official broadcast partner of the 2024 U.S. Open and ESPN+ is where you'll be able to stream the tennis matches online. Watch Fritz vs. Tiafoe live on ESPN+ by signing in with your subscription.
Taylor Swift and Travis Kelce capped off a whirlwind weekend in New York with a trip to Arthur Ashe Stadium for the U.S. Open championship match. Swift and Kelce were filmed arriving to the stadium Sept. 8 before the match officially started at 2 p.m. ET.
The men's final will be on Sunday with coverage on ABC beginning at 2 p.m. ET. The No. 1-ranked Sinner is 34-2 on hard courts in 2024 with four titles, including at the Australian Open in January.
Questions & Answers. 1) Do I have to pay extra to watch the US Open on Prime Video? Prime members in the UK and Ireland can watch the US Open on Prime Video for no additional fees. Non-Prime members can start a 30-day free trial of Prime (£8.99/month or £95/year), or our Prime Video subscription (£5.99/month).
How to watch US Open tennis for free (sort of): While ESPN is a pricey cable channel, US Open coverage will air free in Australia (9Now) and New Zealand (TVNZ+). Even if you're based in the US, you can access free US Open livestream coverage with the help of a VPN.
Jannik Sinner beats Taylor Fritz to win 2024 US Open : NPR. Jannik Sinner beats Taylor Fritz to win 2024 US Open No.1-ranked Sinner, of Italy, prevented Taylor Fritz from ending the American major tennis title drought, less than three weeks after word emerged of Sinner's two positive drug tests.
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