Time: 9h30, Tuesday, January 27, 2015

Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract:  We estimate the pointwise product of two functions in Sobolev spaces \dot{H}^s_q(R^d),  that more general than the Holder's inequality. In the case when s = 0 we get back the usual  Holder inequality. Pointwise multiplication results for Sobolev spaces, which are also probably known in the literature, ([1], [2], and [3]).

Reference

1. J.Y. Chemin Jean-Yves Chemin, Le syst`{e}me de Navier–Stokes incompressible soixante dix ans apr`{e}s Jean Leray, in: Actes des Journ'{e}es Math'{e}matiques `{a} la Mémoire de Jean Leray in: S'{e}min. Congr., vol. 9, Soc. Math. France, Paris, 2004, pp. 99-123.
2. P. G. Lemarie-Rieusset, Recent Developments in the Navier-Stokes Problem Chapman and Hall/CRC Research Notes in Mathematics, vol. 431, Chapman and Hall/CRC, Boca Raton, FL, 2002.
3. T. Kato and H. Fujita: On the non-stationary Navier-Stokes system; Rend. Sem. Mat. Univ. Padova, 32 (1962), 243-260.