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This work intends to prove that strong instabilities may appear for high order geometric optics expansions of weakly stable quasilinear hyperbolic boundary value problems, when the forcing boundary term is perturbed by a small amplitude…
In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous…
Previously, a series of tidally-excited oscillations were discovered in the eccentric eclipsing binary KIC 3230227. The pulsation amplitudes and phases suggest the observed oscillations are prograde quadruple modes. In this paper, we refine…
We study an incompressible viscous flow around an obstacle with an oscillating boundary that moves by a translational periodic motion, and we show existence of strong time-periodic solutions for small data in different configurations: If…
We study a three-dimensional incompressible viscous fluid in a horizontally periodic domain with finite depth whose free boundary is the graph of a function. The fluid is subject to gravity and generalized forces arising from a surface…
Non-stationarity is the rule in the atmospheric boundary layer (ABL). Under such conditions, the flow may experience departures from equilibrium with the underlying surface stress, misalignment of shear stresses and strain rates, and…
We study well-posedness and asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) full von Karman shallow shell equations that accounts for both…
We find three types of steady solutions and remarkable flow pattern transitions between them in a two-dimensional wavy-walled channel for low to moderate Reynolds (Re) and Weissenberg (Wi) numbers using direct numerical simulations with…
Extending work of Texier and Zumbrun in the semilinear non-re ection symmetric case, we study O(2) transverse Hopf bifurcation, or \cellular instability," of viscous shock waves in a channel, for a class of quasilinear hyperbolic{parabolic…
In this paper, we consider an incompressible viscous fluid in an infinitely deep ocean, being bounded above by a free moving boundary. The governing equations are the gravity-driven incompressible Navier-Stokes equations with variable…
Viscous and gravitational fingering refer to flow instabilities in porous media that are triggered by adverse mobility or density ratios, respectively. These instabilities have been studied extensively in the past for 1) single-phase flow…
How fast must an oriented collection of extensile swimmers swim to escape the instability of viscous active suspensions? We show that the answer lies in the dimensionless combination $R=\rho v_0^2/2\sigma_a$, where $\rho$ is the suspension…
We consider localized perturbations to spatially homogeneous oscillations in dimension 3 using the complex Ginzburg-Landau equation as a prototype. In particular, we will focus on heterogeneities that locally change the phase of the…
Fluids in which both time-reversal and parity are broken can display a dissipationless viscosity that is odd under each of these symmetries. Here, we show how this odd viscosity has a dramatic effect on topological sound waves in fluids,…
We study both theoretically and experimentally switching dynamics in surface stabilized ferroelectric liquid crystal cells with asymmetric boundary conditions. In these cells the bounding surfaces are treated differently to produce…
We have explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space (the Cauchy problem). In our presentation, the case of…
The asymptotic frequency $\omega$, dependence of the dynamic viscosity of neutral hard sphere colloidal suspensions is shown to be of the form $\eta_0 A(\phi) (\omega \tau_P)^{-1/2}$, where $A(\phi)$ has been determined as a function of the…
We establish the theoretical framework for adjoint-based phase reduction analysis for incompressible periodic flows. Through this adjoint-based method, we obtain spatiotemporal phase sensitivity fields through a single pair of forward and…
Nonlinear relaxation oscillations of flow-shear induced transport barriers can be qualitatively reproduced using a phenomenological critical-gradient model [M. Leconte, Y.M. Jeon and G.S. Yun, \emph{Contrib. Plasma Phys.} 56, 736 (2016].…
In this note we analyze a model for a unidirectional unsteady flow of a viscous incompressible fluid with time dependent viscosity. A possible way to take into account such behaviour is to introduce a memory formalism, including thus the…