An \(L^q\)-approach to Stokes and Navier-Stokes equations in general domains
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Publication:2495348
DOI10.1007/BF02588049zbMath1111.35033MaRDI QIDQ2495348
Hideo Kozono, Hermann Sohr, Reinhard Farwig
Publication date: 6 July 2006
Published in: Acta Mathematica (Search for Journal in Brave)
Navier-Stokes equations for incompressible viscous fluids (76D05) Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Unnamed Item
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- Unnamed Item
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Weak solutions of Navier-Stokes equations
- On energy inequality, smoothness and large time behavior in L 2 for weak solutions of the Navier-Stokes equations in exterior domains
- Abstract \(L^ p\) estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains
- The Navier-Stokes equations -- a neverending challenge?
- A counter-example concerning the pressure in the Navier-Stokes equations, as \(t\to 0^ +\)
- Global strong solution and its decay properties for the Navier-Stokes equations in three dimensional domains with non-compact boundaries
- On the strong solvability of the Navier-Stokes equations
- Monotonic decreasing and asymptotic behavior of the kinetic energy for weak solutions of the Navier-Stokes equations in exterior domains
- Generalized resolvent estimates for the Stokes system in bounded and unbounded domains
- The initial value problem for the Navier-Stokes equations
- Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine
- Elliptic boundary value problems in unbounded domains with noncompact and nonsmooth boundaries
- Partial regularity of suitable weak solutions of the navier-stokes equations
- REMARK ON UNIQUENESS OF WEAK SOLUTIONS TO THE NAVIER-STOKES EQUATIONS
