Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data

Journal Article · Sat Jan 01 04:00:00 EST 1994 · Communications in Partial Differential Equations; (United States)

DOI:https://doi.org/10.1080/03605309408821042· OSTI ID:7038238

Kozono, Hideo ^[1]; Yamazaki, Masao ^[2]

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1. Nagoya Univ., Chikusa-ku, Nagoya (Japan)
2. 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), Journal Name: Communications in Partial Differential Equations; (United States) Vol. 19:5-6; ISSN CPDIDZ; ISSN 0360-5302
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
CAUCHY PROBLEM
DIFFERENTIAL EQUATIONS
ENERGY TRANSFER
EQUATIONS
HEAT TRANSFER
NAVIER-STOKES EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
QUASILINEAR PROBLEMS
THERMAL CONDUCTION