Instantaneous shrinking of the support of solutions to certain parabolic equations with unbounded initial data
β Scribed by Li Jun-Jie
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 108 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0362-546X
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## Abstract Suppose __u__ is the solution of the initial value problem Suppose __n__ β₯ 1 is odd, __f__ and __g__ are supported in a ball __B__ with boundary __S__, and one of __f__ or __g__ is zero. We derive identities relating the norm of __f__ or __g__ to the norm of the trace of __u__ on __S_
We prove a theorem on stability of a strong solution of the Navier-Stokes equation with respect to perturbation of the initial velocity in the norm of D(A 1/4 ) (where A is the Stokes operator) and also with respect to certain perturbations of the acting body force. The theorem is applied to obtain