Next up for Arsenal and United are FA Cup ties against Leeds United and Wolves, respectively. It is anyone's guess what might happen. In the league, their hopes of finishing in the top four rest on whether they can string together a run of wins but it is a long time since either did that.

United have not won three league games in a row since February. Arsenal have been waiting since October 2018. On this showing Arsenal look more likely.

And as the New Year kicked off in north London, it was Solskjaer's side who began as the form team but you would never have guessed. United's start was so bad that their only killer pass of the first 45 minutes was from David De Gea to Nicolas Pepe to give the Arsenal forward the chance to hit the post from 20 yards.

By that time the visitors could have already been 4-0 down and it was only down to sheer luck and Arsenal's poor finishing that they went in at half-time having only conceded twice. Pepe got the first on eight minutes after Harry Maguire had made sure Sead Kolasinac was onside to cross from the left. The second came when Sokratis Papastathopoulos stabbed in from close range after Alexandre Lacazette had been left unmarked to flick on Pepe's corner from the right.

In between, Pierre-Emerick Aubameyang volleyed over after Pepe had left Luke Shaw in a heap on the floor, Lacazette turned Maguire in the box but made a mess of his finish and Lucas Torreira shot wide from the edge of the area while Fred and Nemanja Matic were still wondering where the Arsenal midfielder had gone.

Buoyant at Burnley, all over the place at Arsenal -- this is Manchester United this season. A new year, but the same problems. Solskjaer does not know which team will turn up. Only Liverpool earned more Premier League points than United in December but this was a display that brought back memories of Bournemouth and Watford.

Arsenal, meanwhile, had conceded at least twice at the Emirates in each of their past five fixtures in all competitions -- their longest run since December 1965 -- and yet were able to keep United out. At Burnley, United looked comfortable in keeping a first clean sheet away from home for 14 matches, but here they looked devoid of any organisation or confidence.

That was partly because of how well Arsenal played. Arteta wants his to team to rush and press and Solskjaer admitted afterwards United had struggled to cope.

"They were the better team," said the United boss. "They were very aggressive."

"The challenge is to maintain it." said Arteta, pointedly, while accepting that the physical demands he has placed on his new players are already taking a toll.

Consistency still eludes Solskjaer, who said: "We always want to build on performances we've had but I can't fault the effort or the drive. It's a hard period. We've been on a good run but we didn't have enough today."

Solskjaer has previously suggested he is already planning for next season while the summer will be the first chance Arteta has to make wholesale changes. Until then the challenge for both men is to eek enough out of their squads to ensure rollercoaster campaigns end with hope their clubs are finally moving in the right direction.