ON THE STOKES EQUATIONS: THE MAXIMUM MODULUS THEOREM

DOI10.1142/S0218202500000537zbMath1019.76016OpenAlexW2026604807MaRDI QIDQ4798829

Paolo Maremonti

Publication date: 16 March 2003

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202500000537

zbMATH Keywords

existenceuniquenessboundary value problemclassical solutionsStokes equationscontinuous dependence on datamaximum modules theorem

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30)

Related Items

Quasi-maximum modulus principle for the Stokes equations, On the \(L^p\) Helmholtz decomposition: a review of a result due to Solonnikov, ON THE TRACTION PROBLEM FOR THE STOKES SYSTEM, A remark on the Stokes problem with initial data in \(L^1\), On the Stokes problem in exterior domains: the maximum modulus theorem, Analyticity of the Stokes semigroup in spaces of bounded functions, A maximum modulus theorem for the Oseen problem, On the Navier-Stokes problem in exterior domains with non decaying initial data, \(L^q\)-solution of the Robin problem for the Stokes system with Coriolis force, Pointwise upper bounds for the solution of the Stokes equation on \(L_\sigma^\infty(\varOmega)\) and applications, Global existence of solutions to 2-D Navier-Stokes flow with non-decaying initial data in exterior domains, A maximum modulus estimate for solutions of the Navier-Stokes system in domains of polyhedral type, Bounded solutions of the Dirichlet problem for the Stokes resolvent system, Conditional stability and periodicity of solutions to evolution equations

Cites Work

• Existence, uniqueness and \(L^ q\)-estimates for the Stokes problem in an exterior domain
• Teorema del massimo modulo e teorema di esistenza e di unicità per il problema di Dirichlet relativo alle equazioni ellittiche in due variabili
• Il teorema del massimo modulo per l'equazione dell'elastostatica tridimensionale
• Mean value formulas, Weyl's lemma and Liouville theorems for \(\Delta^ 2\) and Stokes' system
• On the Stokes problem in Lipschitz domains
• The Dirichlet problem for the Stokes system on Lipschitz domains
• Maximum theorems for solutions of higher order elliptic equations
• On the maximum modulus theorem for stokes functions