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- W2039051630 abstract "We study the Cauchy problem for the incompressible Navier–Stokes equations in two and higher spatial dimensions(0.1)ut−Δu+u⋅∇u+∇p=0,divu=0,u(0,x)=δu0. For arbitrarily small δ>0, we show that the solution map δu0→u in critical Besov spaces B˙∞,q−1 (∀q∈[1,2]) is discontinuous at origin. It is known that the Navier–Stokes equation is globally well-posed for small data in BMO−1 [20]. Taking notice of the embedding B˙∞,q−1⊂BMO−1 (q⩽2), we see that for sufficiently small δ>0, u0∈B˙∞,q−1 (q⩽2) can guarantee that (0.1) has a unique global solution in BMO−1, however, this solution is instable in B˙∞,q−1 and the solution can have an inflation in B˙∞,q−1 for certain initial data." @default.
- W2039051630 created "2016-06-24" @default.
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- W2039051630 date "2015-01-01" @default.
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- W2039051630 title "Ill-posedness for the Navier–Stokes equations in critical Besov spaces <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msubsup><mml:mrow><mml:mover accent=true><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>˙</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mo>∞</mml:mo><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math>" @default.
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- W2039051630 doi "https://doi.org/10.1016/j.aim.2014.09.024" @default.
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