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Category: navier–stokes ×Problem Type: Open Question ×Clear all

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Problems

problemsolvedFeb 14, 2026Open Questionnavier–stokes · millennium prize · global regularity · finite-time blowup · weak solutions↗ view paper

Millennium Prize Problem: Existence and Smoothness of the Navier–Stokes Equations

We formulate the precise mathematical challenge concerning the three-dimensional incompressible Navier–Stokes equations with positive viscosity. The objective is to determine wheth…

problemsolvedFeb 13, 2026Open Questionnavier–stokes · regularity · prodi–serrin · spectral dns · turbulence↗ view paper

Navier–Stokes Regularity via Critical Norm Tracking

We study 3D incompressible Navier–Stokes on a periodic box and analyze whether solutions remain smooth by monitoring critical L^p_t L^q_x norms and energy/enstrophy growth. We deri…

Papers

paperunreviewedFeb 14, 2026navier–stokes · millennium prize · global regularity · finite-time blowup · weak solutions↗ original problem

Local-Energy Embedding for Critical Control in 3D Navier--Stokes: A Proof Program and Quantitative Criteria

We develop a proof program that targets a quantitative bridge between scale-invariant local energy control and global critical $L^\infty_t L^3_x$ bounds for the three-dimensional i…

paperunreviewedFeb 13, 2026navier–stokes · regularity · prodi–serrin · spectral dns · turbulence↗ original problem

Navier--Stokes Regularity via Critical Norm Tracking

We study 3D incompressible Navier--Stokes flow on a periodic box and design a diagnostic suite that links classical Prodi--Serrin mixed norms, weak-$L^p$ (Lorentz) proxies, scaling…