TY - JOUR
T1 - Energy decay for a weak solution of the Navier-Stokes equation with slowly varying external forces
AU - Ogawa, Takayoshi
AU - Rajopadhye, Shubha V.
AU - Schonbek, Maria E.
N1 - Funding Information:
This work was done while the first author visited the University of California, Santa Cruz. He is grateful for the hospitality of UCSC. The work of T. Ogawa is partially supported by the Japan Society for the Promotion of Science. The work of M. E. Schonbek is partially supported by NSF Grant DMS-9020941.
PY - 1997/3
Y1 - 1997/3
N2 - We consider the Navier-Stokes system with slowly decaying external forces[formula]We show that the energy norm of a weak solution has non-uniform decay,||u(t)||2→0 (t→∞),under suitable conditions on the data f and a which make the energy of solution bounded in time. Also, we show the exact rate of the decay (uniform decay) of the energy,||u(t)||2≤C(1+t)-ε,for external forces with a given explicit decay rate.
AB - We consider the Navier-Stokes system with slowly decaying external forces[formula]We show that the energy norm of a weak solution has non-uniform decay,||u(t)||2→0 (t→∞),under suitable conditions on the data f and a which make the energy of solution bounded in time. Also, we show the exact rate of the decay (uniform decay) of the energy,||u(t)||2≤C(1+t)-ε,for external forces with a given explicit decay rate.
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U2 - 10.1006/jfan.1996.3011
DO - 10.1006/jfan.1996.3011
M3 - Article
AN - SCOPUS:0031094014
SN - 0022-1236
VL - 144
SP - 325
EP - 358
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -