On the \(L^p\) Helmholtz decomposition: a review of a result due to Solonnikov

DOI10.1007/s10986-018-9403-6zbMath1411.46025OpenAlexW2892104635MaRDI QIDQ1617264

Paolo Maremonti

Publication date: 7 November 2018

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-018-9403-6

zbMATH Keywords

Helmholtz decompositionfunction spacesspaces of hydrodynamics

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) PDEs in connection with fluid mechanics (35Q35) Stokes and related (Oseen, etc.) flows (76D07) Applications of functional analysis to differential and integral equations (46N20)

Related Items (4)

On the two-dimensional Stokes problem in exterior domains: the maximum modulus theorem ⋮ Well-posedness and regularity for a polyconvex energy ⋮ Some new properties of a suitable weak solution to the Navier-Stokes equations ⋮ A remark on the non-uniqueness in \(L^{\infty}\) of the solutions to the two-dimensional Stokes problem in exterior domains

Cites Work

• Analyticity of the Stokes semigroup in spaces of bounded functions
• On the Helmholtz decomposition in general unbounded domains
• Stokes and Navier-Stokes problems in a half-space: the existence and uniqueness of solutions a priori nonconvergent to a limit at infinity
• Estimates for solutions of nonstationary Navier-Stokes equations
• The Navier-Stokes equations in the weak-\(L^n\) space with time-dependent external force
• The \(L^\infty\)-Stokes semigroup in exterior domains
• Remark on the Helmholtz decomposition in domains with noncompact boundary
• Linear and quasilinear elliptic equations
• General properties of the Helmholtz decomposition in spaces of 𝐿^{𝑞}-type
• ON THE STOKES EQUATIONS: THE MAXIMUM MODULUS THEOREM
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