On the Problem of Maximal $$L^q$$-regularity for Viscous Hamilton–Jacobi Equations

Global regularity for the viscous Boussinesq equations

∇·u=0 Here is the temperature, u=(u1; u2) is the velocity, p is the pressure. In Reference [1], Pumir and Siggia observed that the cap of a symmetric rising bubble collapses in a nite time. In contrast, E and Shu [2] reported that the motion of the bubble cap is a very unlikely candidate for nite time singularity formation. In this paper, we prove the global regularity for the viscous Boussines...

Maximal Regularity for Evolution Equations

Maximal Lp-Regularity for Stochastic Evolution Equations

We prove maximal L-regularity for the stochastic evolution equation

Maximal regularity for nonautonomous evolution equations

We derive sufficient conditions, perturbation theorems in particular, for nonautonomous evolution equations to possess the property of maximal Lp regularity. 1991 Mathematics Subject Classification. 35K90, 47D06.

Maximal L-regularity for Stochastic Evolution Equations

We prove maximal Lp-regularity for the stochastic evolution equation{ dU(t) +AU(t) dt = F (t, U(t)) dt+B(t, U(t)) dWH(t), t ∈ [0, T ], U(0) = u0, under the assumption that A is a sectorial operator with a bounded H∞calculus of angle less than 1 2 π on a space Lq(O, μ). The driving process WH is a cylindrical Brownian motion in an abstract Hilbert space H. For p ∈ (2,∞) and q ∈ [2,∞) and initial...