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- W3100970535 abstract "In this paper we study the Liouville-type properties for solutions to the steady incompressible Euler equations with forces in $${mathbb {R}^N}$$ . If we assume “single signedness condition” on the force, then we can show that a $${C^1 (mathbb {R}^N)}$$ solution (v, p) with $${|v|^2+ |p| in L^{frac{q}{2}}(mathbb {R}^N),,q in (frac{3N}{N-1}, infty)}$$ is trivial, v = 0. For the solution of the steady Navier–Stokes equations, satisfying $${v(x) to 0}$$ as $${|x| to infty}$$ , the condition $${int_{mathbb {R}^3} |Delta v|^{frac{6}{5}} dx < infty}$$ , which is stronger than the important D-condition, $${int_{mathbb {R}^3} |nabla v|^2 dx < infty}$$ , but both having the same scaling property, implies that v = 0. In the appendix we reprove Theorem 1.1 (Chae, Commun Math Phys 273:203–215, 2007), using the self-similar Euler equations directly." @default.
- W3100970535 created "2020-11-23" @default.
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- W3100970535 date "2014-01-24" @default.
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- W3100970535 title "Liouville-Type Theorems for the Forced Euler Equations and the Navier–Stokes Equations" @default.
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- W3100970535 doi "https://doi.org/10.1007/s00220-013-1868-x" @default.
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