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Applying some energy estimates, we show blow-up criteria of strong solutions to the 3D incompressible double-diffusive convection system. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Cauchy problem associated to a magnetic Bénard system in R 3. By using Littlewood–Paley decomposition technique, we provide regularity criteria involving the gradient of the velocity in Vishik spaces, which generalize some well-known results. [ABSTRACT FROM AUTHOR]

We consider a nonlinear eigenvalue problem for equations driven by a weighted (p , q) -Laplacian and a superlinear reaction. We prove a global (with respect to the parameter λ > 0) existence and multiplicity result. We also generate nodal (sign-changing) solutions. Finally, we determine the topological properties of the solution set and prove the continuity properties of the solution multifunction. [ABSTRACT FROM AUTHOR]

In this paper, new classes of functions are defined. These spaces generalize Morrey spaces and give a refinement of Lebesgue spaces. Some embeddings between these new classes are also proved. Finally, the authors apply these classes of functions to obtain regularity results for solutions of partial differential equations of parabolic type. [ABSTRACT FROM AUTHOR]

In this paper, we study the semilinear Korteweg–de Vries equation with time variable coefficients, subject to boundary conditions in a non-parabolic domain. Some assumptions on the boundary of the domain and on the coefficients of the equation will be imposed. The source term and its derivative with respect to t are taken in L 2 (Ω). The existence and uniqueness of the solution is obtained by using the parabolic regularization method, the Faedo–Galerkin and a method based on the approximation of the non-parabolic domain by a sequence of subdomains which can be transformed into regular domains. This paper is an extension of the work Benia and Sadallah (2018). [ABSTRACT FROM AUTHOR]