Related papers: Global existence for a system without self-diffusi…
This article develops and applies results, originally introduced in earlier work, for the existence of homotopy curves, terminating at a desired solution. We describe the principal hypotheses and results in section two; right inverse…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
We develop a global wellposedness theory for weak solutions to the 1D Euler-alignment system with measure-valued density, bounded velocity, and locally integrable communication protocol. A satisfactory understanding of the low-regularity…
We study the Kuramoto-Sivashinsky equation (KSE) in scalar form on the two-dimensional torus with and without advection by an incompressible vector field. We prove local existence of mild solutions for arbitrary data in L2. We then study…
In this manuscript, an attempt has been made to understand the effects of prey-taxis on the existence of global-in-time solutions and dynamics in an eco-epidemiological model, particularly under the influence of slow dispersal characterized…
The global-in-time existence and uniqueness of bounded weak solutions to a spinorial matrix drift-diffusion model for semiconductors is proved. Developing the electron density matrix in the Pauli basis, the coefficients (charge density and…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
The global-in-time existence of renormalized solutions to reaction-cross-diffu-sion systems for an arbitrary number of variables in bounded domains with no-flux boundary conditions is proved. The cross-diffusion part describes the…
This work's major intention is the investigation of the well-posedness of certain cross-diffusion equations in the class of bounded functions. More precisely, we show existence, uniqueness and stability of bounded weak solutions under the…
This article is devoted to the well-posedness of the stochastic compressible Navier Stokes equations. We establish the global existence of an appropriate class of weak solutions emanating from large inital data, set within a bounded domain.…
We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows influenced by interactions with a soluble chemical substance, encompassing the chemotaxis effect, mass transport, and reactions. In the…
We study a nonlinear system coupling the Darcy-Forchheimer-Brinkman equations with a convection-diffusion-reaction equation, arising in reactive transport through porous media. The model features a nonlinear viscosity coupling, Forchheimer…
We investigate the global time existence of smooth solutions for the Shigesada-Kawasaki-Teramoto system of cross-diffusion equations of two competing species in population dynamics. If there are self-diffusion in one species and no…
We prove that the incompressible, density dependent, Navier-Stokes equations are globally well posed in a low Froude number regime. The density is supposed to be increasing in depth and linearized around a stable state. Moreover if the…
In this paper, we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space. The convergence is proved in the sense of probability by introducing an intermediate particle…
The global-in-time existence of weak solutions to a degenerate Cahn-Hilliard cross-diffusion system with singular potential in a bounded domain with no-flux boundary conditions is proved. The model consists of two coupled parabolic…
We study the global well-posedness of a two-dimensional Boussinesq system which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion of type $|\DD|^{\alpha}$ for the temperature. We…
Considered herein is the global existence of weak, strong solutions and Rayleigh-Taylor (RT) instability for 2D semi-dissipative Boussinesq equations in an infinite strip domain $\Omega_{\infty}$ subject to Navier boundary conditions with…
A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state…