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.

UR - http://www.scopus.com/inward/record.url?scp=0031094014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031094014&partnerID=8YFLogxK

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 -