Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data
- Nagoya Univ., Chikusa-ku, Nagoya (Japan)
- Hitotsubashi Univ., Kunitachi, Tokyo (Japan)
In this paper the authors consider a specified Cauchy problem for semilinear hear equations on [Re][sup n] and also the Cauchy problem for the Navier-Stokes equation on [Re][sup n] for n[ge]2 of a specified form. The purpose of the paper is to construct new function spaces in the same way as the Besov spaces, based on the Morrey spaces in place of the standard L[sup p] spaces, and to show that, if the initial data belongs to some function, space above and its norm beings sufficiently small, then the Cauchy problem admits unique time-global solutions with a bound near t = 0. For the Navier-Stokes equation the space where the initial data can be taken are strictly larger than those reported elsewhere. 23 refs.
- OSTI ID:
- 7038238
- Journal Information:
- Communications in Partial Differential Equations; (United States), Vol. 19:5-6; ISSN 0360-5302
- Country of Publication:
- United States
- Language:
- English
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