TY - JOUR
T1 - A remark on Liouville-type theorems for the stationary Navier–Stokes equations in three space dimensions
AU - Kozono, Hideo
AU - Terasawa, Yutaka
AU - Wakasugi, Yuta
N1 - Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2017/1/15
Y1 - 2017/1/15
N2 - Consider the 3D homogeneous stationary Navier–Stokes equations in the whole space R3. We deal with solutions vanishing at infinity in the class of the finite Dirichlet integral. By means of quantities having the same scaling property as the Dirichlet integral, we establish new a priori estimates. As an application, we prove the Liouville theorem in the marginal case of scaling invariance.
AB - Consider the 3D homogeneous stationary Navier–Stokes equations in the whole space R3. We deal with solutions vanishing at infinity in the class of the finite Dirichlet integral. By means of quantities having the same scaling property as the Dirichlet integral, we establish new a priori estimates. As an application, we prove the Liouville theorem in the marginal case of scaling invariance.
KW - Finite Dirichlet integral
KW - Liouville-type theorem
KW - Navier–Stokes equations
KW - Scaling invariance
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U2 - 10.1016/j.jfa.2016.06.019
DO - 10.1016/j.jfa.2016.06.019
M3 - Article
AN - SCOPUS:85002647818
SN - 0022-1236
VL - 272
SP - 804
EP - 818
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -