Resolvent Estimates in Lp for the Stokes Operator in Lipschitz Domains

By Zhongwei Shen. 2012

52 citations recorded by the source corpus.

We establish the Lp resolvent estimates for the Stokes operator in Lipschitz domains in $${\mathbb{R}^d}$$, $${d\geqq 3}$$ for $${|\frac{1}{p}-\frac{1}{2}| < \frac{1}{2d} +\varepsilon}$$. The result implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in Lp for (3/2) − ε < p < 3 + ε. This gives an affirmative answer to a conjecture of M. Taylor (Progr. Nonlinear Differential Equations Appl., vol. 42, pp. 320–334).

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a1c85fb8ffda4275d44857009a1cc42327af1063

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In Applied Mathematics

1. Ken Abe
2. Yoshikazu Giga
3. Matthias Hieber
4. Jürgen Saal
5. Roland Schnaubelt

In Computational Theory and Mathematics

1. Yoshikazu Giga
2. Ken Abe
3. Matthias Hieber

Citations in the corpus

• Stokes Resolvent Estimates in Spaces of Bounded Functions (2012, background): “solvante . 1 2 KEN ABE, YOSHIKAZU GIGA, AND MATTHIAS HIEBER results are known for other type unbounded domains, see [18], [19], [4] ([6], [5] with variable viscosity coefficients) and Lipschitz domains [34]. An L˜p-theory is developed in [14], [15], [16] for a general domain. Moreover, Lp-theory is in”