Since the 1980s, Fourier analysis methods have become of ever greater interest in the study
of linear and nonlinear partial differential equations. In particular, techniques based on …

This series of books forms a unique and rigorous treatise on various mathematical aspects
of fluid mechanics models. These models consist of systems of nonlinear partial differential …

This paper concerns the fluid dynamics modelled by the stochastic flow\left {̇ η\left (t,
x\right)= u\left (t, η\left (t, x\right)\right)+ σ\left (t, η\left (t, x\right)\right) ∘ ̇ W,\\η (0, x)= x …

In this paper, we propose a numerical method based on Wiener Chaos expansion and apply
it to solve the stochastic Burgers and Navier–Stokes equations driven by Brownian motion …

Th i S p ap erst ud i es then O nstati O nary flowofavisco us in CO mp re SS iblefluidin pº
when the initial vo rtici ty is very si ngu l ar. Th e gO V erni ng e qua ti O ns O f mo tion ar ethe …

We prove a uniqueness theorem for the Euler equations for an ideal incompressible fluid
under the condition that vorticity belongs to a space of Besov type. We also prove an …

Long-time solutions to the Navier-Stokes (NS) and Euler (E) equations of incompressible
flow in the whole plane are constructed, under the assumption that the initial vorticity is in L 1 …

We consider the d-dimensional incompressible Euler equations. We show strong
illposedness of velocity in any C m spaces whenever m≥ 1 is an integer. More precisely, we …

Global (in time) solutions of the Navier-Stokes equation, and the associated vorticity
equation, for an incompressible fluid in~ 2 are constructed, with a measure w as the initial …

The well-known quasigeostrophic system (QGS) for zero Rossby number flow has been
used extensively in oceanography and meteorology for modeling and forecasting mid …