(CNN) -- There is a simple message for Michael Schumacher one year on from his devastating accident -- keep fighting.
Formula One's record-breaking, seven-time world champion is continuing his recovery from the severe head injuries he sustained in a skiing crash on 29th December last year.
After emergency brain surgery in France and nine months in hospital, Schumacher has been moved to the family home near Lake Geneva in Switzerland to continue his rehabilitation.
His close family, including his wife Corinna and two teenage children Gina Marie and Mick, have maintained their silent support by choosing not to release a statement on the anniversary of the accident.
Schumacher's son Mick, who is beginning his own racing career in go-karts, had been among the skiing party when the F1 star fell and hit his head on a rock at the French Alps resort of Meribel.
There were expressions of support for Schumacher, however, from the German racer's global fans and members of the F1 community, Monday.
"It has been one year already..." wrote Lotus driver Romain Grosjean on Twitter. "#KeepFightingMichael our thoughts are still with you and your family."
Red Bull driver Daniil Kvyat also marked the occasion: "#KeepFightingMichael -- I know you will."
The Mercedes team, who Schumacher drove for between 2010 and 2012, said: "One year on, our thoughts remain with Michael, his family and friends every day."
Although 12 months have passed since the accident, speculation about Schumacher's condition and its rate of progress remains as intense as ever.
Former F1 racer Philippe Streiff, who was left paralysed during an F1 testing crash in 1989, added grist to the rumor mill in an interview with French newspaper Le Parisien, Sunday.
The Frenchman claimed Schumacher "still has not regained the power of speech....but begins to recognize his own wife and children."
Schumacher's manager Sabine Kehm dismissed the story, telling the Reuters news agency: "I can only confirm that I do not know where Mr Streiff has his information from because he has no contact with us and never has."
Given Schumacher's fame, it is no surprise that public interest in his state of health is unabated.
The German, winner of a record 91 grand prix, was known as fearless racer who gave no quarter on track.
Fans of "Schumi" expect him to continue his fight against his injuries with the same inner steel and determination.
The difficulty with complex head injuries is that there is no predictable prognosis or timeline for recovery.
"If you look at severe head injury victims who go on to make a good recovery -- and I'm not saying all do -- it will always be a story of years," Peter Hamlyn, a consultant neurological and spinal surgeon and expert in the field of head injuries in sport told CNN in June.
In the immediate aftermath of the accident, neurosurgeons operated on Schumacher twice to remove blood clots and reduce swelling on his brain before placing him in a medically induced coma.
A statement from the family in April said the 45-year-old had shown "moments of consciousness and awakening."
In June, it was announced he was out of the coma and would continue his recovery at the University hospital in Lausanne. He was moved to the family home in September.
The latest statement, issued in September, read: "Considering the severe injuries he suffered, progress has been made in the past weeks and months. There is still, however, a long and difficult road ahead.
"We ask that the privacy of Michael's family continue to be respected, and that speculations about his state of health are avoided."
Kehn confirmed to CNN that there was no further update on his medical condition at this time.
Schumacher, who won the F1 drivers' world title with Benetton in 1994 and 1995 before a period of dominance with Ferrari between 2000 and 2004, will turn 46 on 3rd January.
While Schumacher had retired from the sport in 2012, after a second spell with Mercedes, his accident on the ski slopes still sent shockwaves through F1.
But the global sport's close-knit traveling community had to cushion more devastating news in October when Jules Bianchi crashed in the late stages of the Japanese Grand Prix.
The French racer, driving for the now defunct Marussia team, was left with severe head injuries when his car skidded off track in wet conditions and collided with a recovery vehicle.
It was the most serious injury seen in F1 for some years. The last fatalities in F1 were in 1994 when Roland Ratzenberger and three-time world champion Ayrton Senna died on consecutive days at the San Marino Grand Prix.
Bianchi, a promising racer who was part of Ferrari's development academy, is now recovering close to his family home in Nice, France.
The 25-year-old was flown from Japan, where he had been treated in a high dependency unit at Yokkaichi hospital.
"Jules is no longer in the artificial coma in which he was placed shortly after the accident, however he is still unconscious," said the statement released by his parents Philippe and Christine in November.
"He is breathing unaided and his vital signs are stable, but his condition is still classified as 'critical'."
Bianchi, a popular figure on the current F1 grid, is also being remembered during the festive period.
His racing peers Sergio Perez and Kevin Magnussen both tweeted messages of support to Bianchi on Christmas Day.
American racer Alexander Rossi wrote: "As we come to the end of the year, my thoughts and prayers remain with Jules -- teammate, competitor and friend."
As the New Year dawns, Schumacher and Bianchi are both still facing the greatest fights of their lives.