Constructs exact finite-time self-similar blowup solutions for the 1D weak-advection Hou-Li model via fixed-point near origin and ODE extension, for 2/3<a<1 periodic and 0<a≤1 whole-space with Neumann condition.
Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
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abstract
We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with $(-1)$-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.
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math.AP 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Exact Blowup Analysis for the Weak-Advection Hou--Li Model
Constructs exact finite-time self-similar blowup solutions for the 1D weak-advection Hou-Li model via fixed-point near origin and ODE extension, for 2/3<a<1 periodic and 0<a≤1 whole-space with Neumann condition.