American Coco Gauff, the reigning US Open champion, secured a comfortable 6-3, 6-0 win over Slovakia’s Anna Karolina Schmiedlova on Monday to secure a spot in the second round of the Australian Open.

Gauff, 19, traded breaks with Schmiedlova after her opening service game and came up with a late hold to wrap up the first set.

The No. 4 seed stepped up a gear in the second set, as Schmiedlova continued to struggle on serve, and raced ahead 3-0 with a superb cross-court winner from deep to draw loud cheers from the fans on Rod Laver Arena.

Gauff was barely troubled from there as she served out the match, finishing it off with a neat backhand winner to set up a meeting with fellow American Caroline Dolehide in the next round.

Meanwhile, Wimbledon champion Marketa Vondrousova of the Czech Republic was ousted in the first round, beaten 6-1, 6-2 by Ukraine’s Dayana Yastremska.

Vondrousova, the No. 7 seed, missed the Adelaide tune-up event with a hip injury and struggled on serve throughout, hitting seven double faults as she was well-beaten by the world No. 93-ranked player.

Yastremska, who had lost in the first round in her past seven Grand Slam appearances, had 26 winners. During her on-court interview after the match, Yastremska acknowledged the ongoing war in Ukraine and how proud she is of the Ukrainian people. She was emotional in recounting how a rocket had struck her grandmother’s house while she was playing in Brisbane earlier this month.

“I think we just need to remember about it and give as much support as support to Ukraine,” Yastremska said. “But I’m proud to be Ukrainian and thank you everybody for your support.”

In other early play, 19th-seeded Elina Svitolina advanced to the second round, beating Taylah Preston, a wild-card entry from Australia, 6-2, 6-2.

Four-time major winner Naomi Osaka makes her much-anticipated comeback to Grand Slam tennis after the birth of her daughter later Monday. The Japanese player takes on Caroline Garcia of France in the first round in the last match on center court.

US Open champion Coco Gauff says she wants to win at least 10 Grand Slam titles.

She beat Aryna Sabalenka in the final in September to claim her first major title.

Last week the 19-year-old American defended her Auckland Classic title in preparation for the Australian Open, which begins on Sunday.

Asked if she had a number of Grand Slams in mind, Gauff said it would be “cool” to get to “double digits”.

“I don’t know if it will happen, but that’s a high goal,” she said.

“Setting my goals high pushes me beyond what I think I can do.”

Only seven women have won 10 or more Grand Slam singles titles.

Margaret Court holds the record with 24, while Venus Williams’ tally of seven is the highest among current players.

World number four Gauff, who has won 29 of her past 33 matches, is among the favourites to win the Australian Open.

“During the off-season we did celebrate a little bit just because after the US Open everything was so fast,” said Gauff, who faces Slovakia’s Anna Karolina Schmiedlova in the first round in Melbourne on Monday.

“It really feels like so long ago. Some players’ goal is to win a Grand Slam. Once they reach that, it’s kind of ‘what’s next?’

“I always knew I wanted to win multiple.

“The only thing I will try to remember from [the US Open] is just the way that I won. It wasn’t my best tennis. It was more the mental fire.”

In the US Open final Gauff lost the opening set to defending Australian Open champion Sabalenka before fighting back to win 2-6 6-3 6-2.

Coco Gauff may have won her maiden grand slam title at last year’s US Open, but the American youngster already has that particular success in her rear-view mirror.

Not content with just the one major title to her name, the 19-year-old says she is now focused on increasing her grand slam total to at least 10 titles.

“That could change depending on how my career goes. Right now, I would say double digits would be pretty awesome,” Gauff told reporters ahead of this year’s Australian Open.

“I don’t know if it will happen, but I think that’s a high goal. I think setting my goals high pushes me beyond what I think I can do.”

Gauff has long been earmarked as one of tennis’ next superstars after bursting onto the scene as a 15-year-old at Wimbledon almost five years ago.

She has steadily progressed and matured ever since, and eventually clinched her first grand slam title with a comeback win against Aryna Sabalenka at Flushing Meadows in September.

Gauff became the youngest American woman to win the US Open since Serena Williams in 1999, but it’s an achievement she’s keen not to dwell on.

“It was kind of easy to forget about it. Not ‘forget,’ I think that’s the wrong word, maybe just put it in the past and look forward to the future instead of dwelling on the past,” she added.

The American is one of the top contenders for the year’s Australian Open title and says preparation for the tournament hasn’t changed since becoming a grand slam champion.

The youngster is enjoying a patch of good form, having lifted her second consecutive Auckland Classic – and eighth WTA title overall – after beating Elina Svitolina on January 7.

Gauff faces Slovakian Anna Karolína Schmiedlová in the first round in Melbourne and her coach, Brad Gilbert, is confident she can deal with the pressure that comes with being a major winner.

“If you don’t get a little bit better, you fall behind and there’s new young players coming up every year,” Gilbert told CNN Sport’s Don Riddell.

“You can’t control what people say about you, but what you can control is the opponent in front of you and how you compete day in and day out.

“Those are the things that are most important that you need to focus on, not what the media is going to say you’re supposed to do or not supposed to do.”

The Australian Open will begin on January 14 and will run for 15 days until January 28.

Tournament organizers added an extra day to its schedule in a bid to reduce pressure on players and fans following a series of punishing matches in recent years that ended well into the early hours.