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A blow up solution of the Navier-Stokes equations with a super critical forcing term
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abstract
A forced solution $v$ of the axially symmetric Navier-Stokes equation in a finite cylinder $D$ with suitable boundary condition is constructed. The forcing term is in the super critical space $L^q_t L^1_x$ for all $q>1$. The velocity is in the energy space at the final moment when it blows up.
Forward citations
Cited by 2 Pith papers
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A blow up solution of the Navier-Stokes equations with a critical force
Forced Navier-Stokes solutions in the energy space can blow up in finite time under critical-order forces, including an explicit small force in L∞_t L^{3/2}_x.
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A note on the development of singularities on solutions to the Navier-Stokes equations under super critical forcing terms
By multiplying Zhang's self-similar solution by a radial weight r^α, the authors build finite-time blow-up solutions of the forced Navier-Stokes equations with forces in L^q_t L^p_x for all p<2 when q=1.
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