Related papers: Reacting multi-component fluids -- regular solutio…
In this note we consider the motion of a solid body in a two dimensional incompressible perfect fluid. We prove the global existence of solutions in the case where the initial vorticity belongs to $L^p$ with $p>1$ and is compactly…
Classical thermodynamics and statistical mechanics describe systems in which nothing interacts with nothing. Even the highly refined theory of simple fluids does not deal very well with electrical interactions, boundary conditions, or…
It is shown that a hot relativistic fluid could be viewed as a collection of self-interacting quantum objects. They obey a nonlinear equation which is a modification of the quantum equation obeyed by elementary constituents of the fluid. A…
This paper is concerned with the local and global existence of solutions for a generalized $m$-component reaction--diffusion system with a tridiagonal $2$--Toeplitz diffusion matrix and polynomial growth. We derive the eigenvalues and…
We consider a system of nonlinear partial differential equations modeling the unsteady motion of an incompressible generalized Newtonian fluid with chemical reactions. The system consists of the generalized Navier-Stokes equations with…
In this paper, we establish some local and global solutions for the two phase incompressible inhomogeneous flows with moving interfaces in $L_p-L_q$ maximal regularity class. Compared with previous results obtained by V.A.Solonnikov and by…
A class of coupled time-space fractional reaction-diffusion systems derived from reversible chemical reactions over a bounded domain is investigated. Employing mainly an appropriate Lyapunov functional and an improved maximum principle, we…
Multi-component fluid flow simulations in multi-scale porous structures often involve regions that are under-resolved at practical computational resolutions. Accurately capturing the contributions from these unresolved regions is critical.…
This paper is devoted to the study of the regularity of solutions to some systems of reaction--diffusion equations, with reaction terms having a subquadratic growth. We show the global boundedness and regularity of solutions, without…
Our current understanding of the Universe depends on the interplay of several distinct "matter" components, which interact mainly through gravity, and electromagnetic radiation. The nature of the different components, and possible…
The implementation of boundary conditions is among the most challenging parts of modeling fluid flow through channels and complex media. Here, we show that the existing methods to deal with liquid-wall interactions using multicomponent…
We consider viscous, heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of…
The close-to-equilibrium regularity of solutions to a class of reaction-diffusion systems is investigated. The considered systems typically arise from chemical reaction networks and satisfy a complex balanced condition. Under some…
We are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a general theory on the well-posedness of…
In this paper, we study non-Newtonian fluids in a class of unbounded domains with noncompact boundaries. With respect to the resulting mathematical problems, we establish the global existence of solutions with arbitrary large flux under…
Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the…
We present a thermodynamically consistent theoretical framework for lyotropic liquid crystals (LCs) based on the GENERIC (General Equation for the Non-Equilibrium Reversible-Irreversible Coupling) formalism. This formalism ensures…
One-dimensional quantum fluids are conventionally described by using an effective hydrodynamic approach known as Luttinger liquid theory. As the principal simplification, a generic spectrum of the constituent particles is replaced by a…