| Abstract: |
| In this talk we will show that for arbitrarily prescribed finite energy divergence-free initial data, there exist infinitely many global-in-time weak solutions with continuous energy profiles to both the 3D deterministic and stochastic Navier-Stokes equations. When the initial data is in $H^1/2$, we prove the existence of infinitely many dissipative solutions to the 3D Navier-Stokes and MHD equations, whose energy profiles are continuous and decreasing on time. Our proof introduces a new backward convex integration scheme that takes advantage of the dissipative term. |
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