London, Oct 7: A mathematician from Lehigh University in Bethlehem, Pennsylvania, has reportedly found a smooth solution to the three-space dimensional Navier-Strokes system, which has for long been considered to be one of mathematics' greatest unsolved problems.

If the papers authored by Penny Smith prove correct, she can lay claim to one million dollars in prize money from the Clay Mathematics Institute, based in Cambridge, Massachusetts, which had listed Navier-Stokes problem among its seven Millennium Prize Problems in 2000.

The Navier-Stokes equations describe how a fluid flows, and they are derived by applying Newton's laws of motion to the flow of an incompressible fluid, and adding in a term that accounts for energy lost through the liquid equivalent of friction, viscosity.

She says that she began working on this problem one month ago, after somebody asked her to work on one of the clay problems.

"Somebody asked me why don't I work on one of the Clay problems. So I looked around for one to do with differential equations," Nature magazine quoted her as saying.

Smith says that she started feeling very insecure right from the moment she posted the paper online, but after revising them she became confident about the viability of her findings.

"I'm pretty confident that my result is right, or I would never have submitted it anywhere," she says.

However, experts in the field say that it is too early to make a call on whether the paper is correct.

Charles Fefferman, a Princeton University mathematician amongst the experts who are looking at Smith’s paper, says that they have seen about half-a-dozen such papers in the past, most of which were found to have fatal errors.

He expects that assessment of Smith's work will take more time than the earlier assessments, as it relies heavily on her earlier publications, and he will have to trawl through them too.

Fefferman says that Smith’s earlier papers are in peer-reviewed journals or are listed as "to appear" in such journals, so he can believe them to be correct, but her claims of having solved navier-stokes equations cannot be taken lightly.

"That increases the probability that they're right, but for something this important I wouldn't trust that," he says.

James Carlson, president of the Clay Mathematics Institute, says that he is seeking expert opinions on the paper, but adds, "It is far too early to say whether it is correct or not."

He says that to win the prize, Smith's work will have to withstand two years of scrutiny after appearing in a peer-reviewed journal. (ANI)