254A, Notes 1: Local well-posedness of the Navier-Stokes equations | What's new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao 16 September, 2018 in 254A - Incompressible fluid equations, math.AP | Tags: local wellposedness | by Terence Tao We now begin the rigorous theory of the incompressible Navier-Stokes equations In order for the system (1) to even make sense, one requires some level of regularity on the unknown fields ; this turns out to be a relatively important technical issue that will require some attention later in this set of notes, and we will end up transforming (1) into other forms that are more suitable for lower regularity candidate solution. Our focus here will be on local existence of these solutions in a short time interval or , for some . (One could in principle also consider solutions that extend to negative times, but it turns out that the equations are not time-reversible, and the forward evolution is significantly more natural to study than the backwards one.) The
254A, Notes 1: Local well-posedness of the Navier-Stokes equations | What's new What's new Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao Home About Career advice On writing Books Mastodon+ Applets Subscribe to feed 254A, Notes 1: Local well-posedness of the Navier-Stokes equations 16 September, 2018 in 254A - Incompressible fluid equations , math.AP | Tags: local wellposedness | by Terence Tao We now begin the rigorous theory of the incompressible Navier-Stokes equations where is a given constant (the kinemat
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