On a free boundary problem for the Navier-Stokes equations

By Yoshihiro Shibata, Senjo Shimizu. Differential and Integral Equations, 2007

56 citations recorded by the source corpus.

In this note, we consider a free boundary problem for tbe Navier-Stokes equation in several domains in $\mathbb{R}^{n}(n\geq 2)$ with surface tension. We will state a local in time unique existence theorem in the space $W_{q,p}^{2,1}$ $(2<p<\infty$ and $n<q<\infty)$ , which is proved by using the maximal regularity theorem of the corresponding linearized problem. Also, we state the resolvent estimate, the generation of analytic semigroup and the maximal regularity theorem of the corresponding linearized problem.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/3d888da20eb07ac4a293e41124ae7688717a3da7

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In Applied Mathematics

1. Yoshihiro Shibata
2. Senjo Shimizu
3. Rieko Shimada
4. Matthias Hieber
5. Ryo Ikehata

In Computational Theory and Mathematics

1. Yoshihiro Shibata
2. Senjo Shimizu
3. Rieko Shimada
4. Ryo Ikehata
5. Matthias Hieber

Citations in the corpus

• On the maximal $L_p$-$L_q$ regularity of the Stokes problem with first order boundary condition; model problems (2012, methodology): “¤ By Lemma 3.5 and the Leibniz formula, we have ∣∣∣∣Dαξ ( iξj λe−²|ξ| 2 P (ξ) λ + µ|ξ|2 )∣∣∣∣ ≤ Cα,σ,µ|ξ|1−|α|, ∣∣∣∣Dαξ { τ ∂ ∂τ ( iξj λe−²|ξ| 2 P (ξ) λ + µ|ξ|2 )}∣∣∣∣ ≤ Cα,σ,µ|ξ|1−|α| for j = 1, . . . , n and (λ, ξ) ∈ Σσ,0 × (Rn \ {0}), which combined with Lemma 3.6 below due to Shibata and Shimizu”
• General Parabolic Mixed Order Systems in Lp and Applications (2013, unknown): “[EPS03], [BP07], [GR07], [PSS07], [SS07], [PS09], [PS10], [DGH11], [SS11b].”