Related papers: A regularity criterion for the dissipative quasi-g…
We consider a combination of local and nonlocal $p$-Laplace equations and discuss several regularity properties of weak solutions. More precisely, we establish local boundedness of weak subsolutions, local H\"older continuity of weak…
We consider regularity properties of stochastic kinetic equations with multiplicative noise and drift term which belongs to a space of mixed regularity ($L^p$-regularity in the velocity-variable and Sobolev regularity in the…
In this paper we establish a Serrin type regularity criterion on the gradient of pressure in weak spaces for the Leray-Hopf weak solutions of the Navier-Stokes equations in R3.
This article is devoted to the analysis of necessary and/or sufficient conditions for metric regularity in terms of Demyanov-Rubinov-Polyakova quasidifferentials. We obtain new necessary and sufficient conditions for the local metric…
In the present study, we find that the surface quasi-geostrophic equation admits exact solutions, which evolve with time in quasi-stationary states. The solutions presented are available for any dissipation effect $\kappa (-\Delta)^\alpha$…
We consider the evolution of weak vanishing viscosity solutions to the critically dissipative surface quasi-geostrophic equation. Due to the possible non-uniqueness of solutions, we rephrase the problem as a set-valued dynamical system and…
The paper deals with the problem of the energy conservation for the weak solutions to the compressible Primitive Equations (CPE) system with degenerate viscosity. The sufficient conditions on the regularity of weak solutions for the energy…
A new weak existence result for degenerate multi-dimensional stochastic McKean--Vlasov equation is established under relaxed regularity conditions.
We establish existence results for a class of mixed anisotropic and nonlocal $p$-Laplace equation with singular nonlinearities. We consider both constant and variable singular exponents. Our argument is based on an approximation method. To…
This article proves the existence and regularity of weak solutions for a class of mixed local-nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central…
We consider a quasilinear parabolic stochastic partial differential equation driven by a multiplicative noise and study regularity properties of its weak solution satisfying classical a priori estimates. In particular, we determine…
We establish new sufficient conditions for the existence of weak Besicovitch quasiperiodic solutions for natural Lagrangian system on Riemannian manifold with time-quasiperiodic force function
This work is devoted to study the relation between regularity and decay of solutions of some dissipative perturbations of the Korteweg-de Vries equation in weighted and asymmetrically weighted Sobolev spaces.
In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.
In this paper, we establish some $\varepsilon$-regularity criteria in anisotropic Lebesgue spaces for suitable weak solutions to the 3D Navier-Stokes equations as follows: $$ \limsup\limits_{\varrho\rightarrow0}…
In this note, we establish the interior $BMO$ regularity of weak solutions to uniformly elliptic equations in divergence form. Moreover, the assumptions on the coefficients are nearly optimal.
The initial value problem for the two dimensional dissipative quasi-geostrophic equation of the critical and the supercritical cases is considered. Anomalous diffusion on this equation provides slow decay of solutions as the spatial…
We present some new regularity criteria for suitable weak solutions of magnetohydrodynamic equations near boundary in dimension three. We prove that suitable weak solutions are H\"older continuous near boundary provided that either the…
Here we develop a method for investigating global strong solutions of partially dissipative hyperbolic systems in the critical regularity setting. Compared to the recent works by Kawashima and Xu, we use hybrid Besov spaces with different…
We propose a new approach to models of general compressible viscous fluids based on the concept of dissipative solutions. These are weak solutions satisfying the underlying equations modulo a defect measure. A dissipative solution coincides…