The initial value problem for the Boussinesq equations with data in \(L^p\). (English) Zbl 0429.35059

Cannon, J. R.; DiBenedetto, Emmanuele

Approximation methods for Navier-Stokes problems, Proc. Symp. IUTAM, Paderborn 1979, Lect. Notes Math. 771, 129-144 (1980).

MSC:

35Q30	Navier-Stokes equations
35A01	Existence problems for PDEs: global existence, local existence, non-existence
35A02	Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
76D05	Navier-Stokes equations for incompressible viscous fluids
76R05	Forced convection
80A20	Heat and mass transfer, heat flow (MSC2010)
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
45E10	Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)

Keywords:

existence and uniqueness; Cauchy problem; Boussinesq model; viscous incompressible fluid; heat transfer; embedding theorem; singular integral operators; regularity