Five Britons in first-round action on day three in New York
LIVE: Billy Harris 4-6 Felix Auger-Aliassime
LIVE: Fran Jones 0-6 Germany's Eva Lys
Sonay Kartal also out after 6-3 1-6 6-1 defeat by Beatriz Haddad Maia
Jacob Fearnley takes on Roberto Bautista Agut later on Tuesday
Men's defending champion Jannik Sinner beats Vit Kopriva 6-1 6-1 6-2; Iga Swiatek wins 6-1 6-2 against Emiliana Arango
Listen to BBC Radio 5 Sports Extra coverage at top of page (UK only)
*Boulter 4-6 3-5 Kostyuk
Katie Boulter once again saves match point as Marta Kostyuk misses the forehand.
A loose forehand flies into the net, though, and we go again.
Fourth match point.
Image source, Getty Images*Boulter 4-6 3-5 Kostyuk
Leon Smith
GB Davis Cup captain on BBC Radio 5 Sports Extra and BBC Sounds
There's been a bit of anger and frustration in Katie Boulter's last couple of points. She is pretty much playing her best tennis now.
She has been chirping a bit at her player box, which isn't like her, so that shows she is frustrated because she knows she can play at a higher level than this.
*Boulter 4-6 3-5 Kostyuk
All that good work but the serve demons return.
Katie Boulter follows up saving two match points with a double fault.
A third look at match point for Marta Kostyuk.
*Haddad Maia 6-3 1-6 0-0 Kartal
What a fighter. You can never, ever count Sonay Kartal out of any match.
A tremendous set of tennis from the Briton and she takes 18th seed Beatriz Haddad Maia into a decider.
*Boulter 4-6 3-5 Kostyuk
Katie Boulter saves the first match point as Marta Kostyuk misses the forehand then a powerful volley wipes out the second.
Deuce.
Image source, Getty Images*Boulter 4-6 3-5 Kostyuk
Oh no. That's a seventh double fault of the match for Katie Boulter and it hands her opponent two match points.
Jonathan Jurejko
BBC Sport senior tennis reporter at Flushing Meadows
Image source, BBC SportKatie Boulter still has not lost belief judging by her constant cajoling and fist pumps.
But time is, of course, running out.
Sweltering, by the way, at Flushing Meadows. A few US Open-issued towels are covering heads.
*Boulter 4-6 3-5 Kostyuk
Katie Boulter throws down her racquet in frustration as she goes down 0-30 on her serve. A bit of a crack in the usually positive attitude that we see from Boulter.
She lets out a roar of relief as she wins the next point.
Haddad Maia 6-3 1-5 Kartal*
That is a rocket of a forehand return from Sonay Kartal!
Beatriz Haddad Maia somehow picks it up off the baseline but can't get it back in play and that's a double break for the British number three.
Kartal is serving to level the match.
*Boulter 4-6 3-5 Kostyuk
Marta Kostyuk holds her nerve to see out the hold and put herself within one game of winning the match.
Boulter 4-6 3-4 Kostyuk*
Leon Smith
GB Davis Cup captain on BBC Radio 5 Sports Extra 2 and BBC Sounds
A very important service hold for Katie Boulter, it just keeps her in the match here.
You never know what might happen so you have to ask the questions. She isn't too far away at 4-3 down because one break of serve and she is right back in it.
If she gets a good feeling of the ball, she can do this.
Boulter 4-6 3-4 Kostyuk*
Image source, Getty ImagesMarta Kostyuk has hit eight aces today. And she has won all four of the break points she has earned.
Meanwhile Katie Boulter has hit six double faults and hit just seven winners to Kostyuk's 17.
That seems to be the difference so far.
*Haddad Maia 6-3 1-4 Kartal
Onto the fourth deuce of the game and Beatriz Haddad Maia goes wide with a backhand.
Another chance for a double break for Sonay Kartal...
Arango 1-6 2-3 Swiatek*
Iga Swiatek is far too strong on her own serve.
She holds again with the loss of just one point and asks even more questions of Emiliana Arango.
The Colombian finds the answers though as she responds with a hold to love to keep herself in this contest.
Can she find the break back?
Image source, Getty ImagesBoulter 4-6 3-4 Kostyuk*
Katie Boulter takes another no-nonsense hold, this time to 15.
Marta Kostyuk will serve to put herself one game away from reaching the second round so Boulter needs to dig deep here to find something.
She has looked pretty sticky at times.
Musetti 6-7 (3-7) 6-3 0-0 Mpetshi-Perricard*
Tenth seed Lorenzo Musetti is finding his feet in this match and levels up the score by taking the second set against Frenchman Giovanni Mpetshi-Perricard.
Mpetshi-Perricard, who is renowned for his thunderbolt serve, didn't drop a point on his first serve in that set but his second serve was much less reliable, and his opponent managed to convert what has been the only break point of the match so far.
*Haddad Maia 6-3 1-4 Kartal
Leon Smith
GB Davis Cup captain on BBC Radio 5 Sports Extra 2 and BBC Sounds
Image source, Getty ImagesSonay's played so much better in this second set. She's got Haddad Maia moving more and she's playing much more into the Haddad Maia backhand, so she's unable to attack with her forehand like she did in the first set.
She's stayed very relaxed and she needs to be with the way she hits the ball with a lot of racquet speed, spin and variety.
Haddad Maia is a great fighter. You wouldn't know what the score is from this set in terms of her body language. It's very positive. She will fight, but she's certainly not hitting the ball well.
*Haddad Maia 6-3 1-4 Kartal
Once again, Beatriz Haddad Maia makes a good start to a service game but then gifts Sonay Kartal a break point with three consecutive unforced errors.
Kartal gets a look at a second serve but sends her return a fraction long.
A big roar from the Brazilian as she drills a cross-court backhand for a winner, but Kartal takes control of the next point with some powerful groundstrokes.
Another deuce to come...
*Boulter 4-6 2-4 Kostyuk
Marta Kostyuk takes another convincing hold and restores that two-game cushion.
She still has that break advantage under her belt. Katie Boulter is going to have to make her move pretty quickly as this one begins to slip away from her.
Image source, Getty ImagesArango 1-6 1-2 Swiatek*
A hold to love for Iga Swiatek piles the pressure on her opponent.
Emiliana Arango responds though and sees out her service game with an ace.
It's not all over just yet.
