On the $${\mathscr {R}}$$ R -Bounded Solution Operator and the Maximal $$L_p$$ L p - $$L_q$$ L q Regularity of the Stokes Equations With Free Boundary Condition

DOI10.1007/978-4-431-56457-7_9zbMath1373.35224OpenAlexW2559553833MaRDI QIDQ5278251

Yoshihiro Shibata

Publication date: 13 July 2017

Published in: Mathematical Fluid Dynamics, Present and Future (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-4-431-56457-7_9

zbMATH Keywords

Stokes systemanalytic semigroupfree boundary conditionmaximal \(L^p-L^q\) regularity

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Free boundary problems for PDEs (35R35)

Related Items (12)

Maximal \(L^p-L^q\) regularity for two-phase fluid motion in the linearized Oberbeck-Boussinesq approximation ⋮ On the local wellposedness of free boundary problem for the Navier-Stokes equations in an exterior domain ⋮ On the Stokes system in cylindrical domains ⋮ The \(\mathcal{R}\)-bounded operator families arising from the study of the barotropic compressible flows with free surface ⋮ Stability of stationary solutions to the three-dimensional Navier-Stokes equations with surface tension ⋮ Local well-posedness for two-phase fluid motion in the Oberbeck-Boussinesq approximation ⋮ Global well-posedness of unsteady motion of viscous incompressible capillary liquid bounded by a free surface ⋮ ℛ $${\mathcal R}$$ Boundedness, Maximal Regularity and Free Boundary Problems for the Navier Stokes Equations ⋮ Strong solutions to compressible-incompressible two-phase flows with phase transitions ⋮ Compressible-incompressible two-phase flows with phase transition: model problem ⋮ On periodic solutions for one-phase and two-phase problems of the Navier-Stokes equations ⋮ Local well-posedness of incompressible viscous fluids in bounded cylinders with \(90^\circ \)-contact angle

Cites Work

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• \(L_p\)-estimates for a linear problem arising in the study of the motion of an isolated liquid mass
• On the maximal \(L_{p}\)-\(L_{q}\) regularity of the Stokes problem with first order boundary condition; model problems
• On the two-phase Navier-Stokes equations with surface tension
• Trace operators in Besov and Triebel-Lizorkin spaces
• Generalized resolvent estimates of the Stokes equations with first order boundary condition in a general domain
• On the \(\mathcal {R}\)-boundedness of solution operators for the Stokes equations with free boundary condition.
• On some free boundary problem of the Navier-Stokes equations in the maximal \(L_p - L_q\) regularity class
• On the global well-posedness of strong dynamics of incompressible nematic liquid crystals in \(\mathbb R^N\)
• Moving Interfaces and Quasilinear Parabolic Evolution Equations
• Analytic Solutions for the Two-phase Navier-Stokes Equations with Surface Tension and Gravity
• On the existence for the Cauchy-Neumann problem for the Stokes system in the $L_p$-framework
• On the $\mathcal{R}$-Sectoriality and the Initial Boundary Value Problem for the Viscous Compressible Fluid Flow
• Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity

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