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Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle

Reinhard Farwig (2005)

Banach Center Publications

Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space ℝ³. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper [2] the author proved $L^{q}$ -estimates of second order derivatives uniformly in the angular and translational velocities, ω and...

Étude de l’équation $\frac{1}{2} Δ u - u μ = 0$ où $μ$ est une mesure positive

Denis Feyel, A. de La Pradelle (1988)

Annales de l'institut Fourier

On montre que les solutions faibles de l’équation $Δ u - u μ = 0$ , où $μ$ est une mesure positive négligeant les polaires, vérifient une inégalité de Harnack. On s’occupe également des sursolutions dont on fait la représentation intégrale a l’aide d’une fonction de Green. Comme les solutions sont discontinues, on est amené à utiliser les formules probabilistes.

Evolution operators for higher order abstract parabolic equations

Enrico Obrecht (1986)

Czechoslovak Mathematical Journal

Evolutionary equation of inertial waves in 3-D multiply connected domain with Dirichlet boundary condition.

Krutitskii, Pavel A. (2001)

International Journal of Mathematics and Mathematical Sciences

Exact solutions of Cauchy problem for partial differential equations with double characteristics and singular coefficients

Zhu-Jia Lu (1996)

Mathematica Bohemica

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

Dimovski, Ivan, Tsankov, Yulian (2012)

Mathematica Balkanica New Series

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05In this paper a method for obtaining exact solutions of the multidimensional heat equations with nonlocal boundary value conditions in a finite space domain with time-nonlocal initial condition is developed. One half of the space conditions are local, and the other are nonlocal. Extensions of Duhamel principle are obtained. In the case when the initial value condition is a local one i.e. of the form u(x1; :::; xn; 0) = f(x1; :::; xn) the problem reduces...