The High Court has heard that there is no reasonable prospect that an unborn child will survive, even if the mother's life support is continued.
The woman at the centre of this case was admitted to a hospital outside Dublin on November 27 when she was 14 weeks pregnant with her third child.
She presented with severe headaches. Her condition quickly deteriorated and she was transferred to a hospital in Dublin where she did not survive surgery on her brain. On December 3, she was declared brain dead.
Her family and the father of the child want life support to be switched off, but doctors were concerned about the Constitutional right to life of the unborn child.
The court heard evidence today from three obstetricians and three other doctors, who are all in agreement that continuing life support is not in the best interests of the woman and that the baby is very unlikely to be born healthy.
The prospects for the child's survival thereafter are said to be "very poor".
The Health Service Executive (HSE) told the special sitting of the High Court that it does not object to "somatic support" being switched off, as there is no reasonable prospect for the child being born alive even if life support is continued.
Consultant obstetrician Dr Peter Boylan told the court that legal guidelines would be helpful to doctors, but that repealing the 8th amendment would be even more helpful.
He said the child was effectively in intensive care in the mother's womb, and continuing life support in this case was "experimental" and placed doctors in "uncharted territory".
The case will continue tomorrow, and the judge said the court would make its decision on St Stephen's Day.