As the trial entered its 10th day, a day when a respected medical expert told the jury Mr Floyd had been killed as a result of the way he was held down by Minneapolis police officers and was thus robbed of oxygen, Rodney Floyd said he was impressed by the witnesses who had spoken, and what they had said.
Yet, he said all he and other relatives and supporters of the man whose death last year sparked international outcry, could do was to stick together and hope the jury delivered what they considered a just verdict.
“The evidence is coming out, witnesses are stepping forward – great witnesses,” Rodney Floyd, one of the brothers of the man who was killed last May outside a convenience store, told The Independent as he entered court.
He added: “But again, you know, the case is up to the jury. But the the case is going great.”
Mr Chauvin, 45, is one of four former Minneapolis police officers who were fired, and then arrested and charged, over the killing of Mr Floyd on May 25 last year.
The officer was notoriously captured on cellphone footage taken by bystanders, kneeling on Mr Floyd’s neck for more than nine minutes. During that time, Mr Floyd, who was originally from Texas and had five children, could be heard to say: “I cannot breathe.”
Mr Chauvin is charged with second-degree murder, third-degree murder and manslaughter, after detaining Mr Floyd outside a neighbourhood market when he was accused of trying to pass a counterfeit $20 bill.
Three other officers have also been charged and their trials are set to follow that of Mr Chauvin. Depending on the verdicts, federal authorities may also wish to charge the men.
Last month, before the trial started, the city of Minneapolis agreed to pay $27m to settle a civil lawsuit from George Floyd’s family over his death in police custody.
Council members met privately to discuss the settlement, then returned to public session for a unanimous vote in support of the massive payout, that easily surpassed the $20m the city approved two years ago to the family of a white woman killed by a police officer.
Mr Floyd had three brothers, Rodney, Terrence and Philonise Floyd. Various members of the family, including nephew Brandon Williams, have been attending the trial at the court at the Hennepin County Government Centre, in the centre of Minneapolis.
The entire complex has been sealed off by fencing, security is heavy, and other workers have been sent home for the duration. Hennepin County Judge Peter Cahill ruled that the trial should be televised, the first time for the state of Minnesota.
He did so over the objections of the prosecution, but argued it was essential given the pandemic, saying people could not otherwise have the chance to follow such an important case.
On Friday, the court was told that Mr Floyd had died of a lack of oxygen from the way he was held down by police.
Lindsey Thomas, who retired in 2017 from the Hennepin County Medical Examiner's office in Minneapolis, bolstered the findings of other experts on Thursday who rejected the defence theory that Mr Floyd's drug use and underlying health problems killed him.
Dr Thomas did not work on Mr Floyd's case but she said she agreed with her former colleague, Hennepin County Medical Examiner Andrew Baker, who had said he died from cardiopulmonary arrest complicated by the way law enforcement restrained him and compressed his neck.
She actually went further, saying “the primary mechanism of death is asphyxia, or low oxygen”.
“This is a death where both the heart and lungs stopped working. The point is, it's due to law enforcement subdual, restraint and compression,“ she said. ”The activities of the law enforcement officers resulted in Mr Floyd's death.”
Mr Floyd’s brother said he and other members of the family were trying to keep their spirits up, as the case played out.
What did he want the rest of the trial to bring out?
“Stay strong, stay [united],”he said.
“Stay supportive, and just, again, we’ve just got to wait for the outcome. We’ve got to the wait for the jury.”
Additional reporting by the Associated Press