# AnLq-approach to Stokes and Navier-Stokes equations in general domains

@article{Farwig2005AnLqapproachTS, title={AnLq-approach to Stokes and Navier-Stokes equations in general domains}, author={Reinhard Farwig and Hideo Kozono and Hermann Sohr}, journal={Acta Mathematica}, year={2005}, volume={195}, pages={21-53} }

## 142 Citations

### On partial regularity of suitable weak solutions to the Navier–Stokes equations in unbounded domains

- Mathematics, Philosophy
- 2008

Consider the nonstationary Navier–Stokes equations in Ω × (0, T), where Ω is a general unbounded domain with non-compact boundary in R3. We prove the regularity of suitable weak solutions for large…

### Maximal $L_p$-$L_q$ regularity for the Stokes equations with various boundary conditions in the half space

- Mathematics
- 2022

We prove resolvent L p estimates and maximal L p - L q regularity estimates for the Stokes equations with Dirichlet, Neumann and Robin boundary conditions in the half space. Each solution is…

### Unique solvability of elliptic problems associated with two-phase incompressible flows in unbounded domains

- MathematicsDiscrete & Continuous Dynamical Systems
- 2021

This paper shows the unique solvability of elliptic problems associated with two-phase incompressible flows, which are governed by the two-phase Navier-Stokes equations, in unbounded domains such as…

### The Minkowski dimension of interior singular points in the incompressible Navier--Stokes equations

- Mathematics
- 2016

### Stability with respect to domain of the low Mach number limit of compressible viscous fluids

- Mathematics, Physics
- 2013

We study the asymptotic limit of solutions to the barotropic Navier–Stokes system, when the Mach number is proportional to a small parameter e → 0 and the fluid is confined to an exterior spatial…

### On the Vanishing Electron-Mass Limit in Plasma Hydrodynamics in Unbounded Media

- MathematicsJ. Nonlinear Sci.
- 2012

This work considers the zero-electron-mass limit for the Navier–Stokes–Poisson system in unbounded spatial domains and shows that the asymptotic limit is represented by the incompressible Navier-Stokes system, with a Brinkman damping, in the case when viscosity is proportional to the electron-mass.

## References

SHOWING 1-10 OF 29 REFERENCES

### On energy inequality, smoothness and large time behavior inL2 for weak solutions of the Navier-Stokes equations in exterior domains

- Mathematics
- 1988

Soit Ω un domaine exterieur de R n (n=3,4) a frontiere lisse ∂Ω. Sur le cylindre d'espace temps Ω×[0,∞) on considere le probleme de Navier-Stokes non stationnaire: u t −Δu+u•⊇u+⊇p=f dans Ω×(0,∞),…

### Sur le mouvement d'un liquide visqueux emplissant l'espace

- Mathematics
- 1934

### Elliptic boundary value problems in unbounded domains with noncompact and nonsmooth boundaries

- Mathematics
- 1986

SuntoSi studia la risolubilità e l'unicità inLp (1<p<+∞) della soluzione di problemi al contorno ellittici in domini illimitati la cui frontiera contiene un numero finito di punti angolosi.SummaryWe…

### PARTIAL DIFFERENTIAL EQUATIONS

- Mathematics
- 1941

Introduction Part I: Representation formulas for solutions: Four important linear partial differential equations Nonlinear first-order PDE Other ways to represent solutions Part II: Theory for linear…

### REMARK ON UNIQUENESS OF WEAK SOLUTIONS TO THE NAVIER-STOKES EQUATIONS

- Mathematics
- 1996

(N-S) du — Au + u • Vu + Vp = / in χ e Ω, 0 < t < Τ, at div u = 0 in χ e Ω, 0 < t < Τ, u = 0 on 3Ω, w|t=o a, where u = u(x,t) = («'(χ, i), · · •, u(x, t)) and ρ = p(x,t) denote the unknown velocity…

### Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine

- Mathematics
- 1964

### On the Strong Solvability of the Navier—Stokes Equations

- Mathematics
- 2000

Abstract. In this paper we study the strong solvability of the Navier—Stokes equations for rough initial data. We prove that there exists essentially only one maximal strong solution and that various…