Blowup of classical solutions to the pressureless Euler/isentropic Navier‐Stokes equations
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5859
Abstract: In this paper, we will show the blowup of classical solutions to the Cauchy problem for the pressureless Euler/isentropic Navier‐Stokes equations in arbitrary dimensions under some restrictions on the initial data. Compared with the degenerate… read more here.
Keywords: classical solutions; navier stokes; isentropic navier; pressureless euler ... See more keywords
On Classical Solutions for Viscous Polytropic Fluids with Degenerate Viscosities and Vacuum
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DOI: 10.1007/s00205-019-01412-6
Abstract: In this paper, we consider the three-dimensional isentropic Navier-Stokes equations for compressible fluids with viscosities depending on density in a power law and allowing initial vacuum. We introduce the notion of regular solutions and prove… read more here.
Keywords: solutions viscous; viscous polytropic; vacuum; initial data ... See more keywords
Existence of classical solutions of quasi-linear non-cooperative elliptic systems
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DOI: 10.1007/s11868-016-0167-7
Abstract: Method of sub- and super-solutions is applied in investigation of solvability in classical $$C^2(\Omega ) \bigcap C(\overline{\Omega })$$C2(Ω)⋂C(Ω¯) sense of quasi-linear non-cooperative weakly coupled systems of elliptic second-order PDE. The result is illustrated on a… read more here.
Keywords: non cooperative; linear non; solutions quasi; classical solutions ... See more keywords
Boundedness of classical solutions for a chemotaxis model with consumption of chemoattractant
Sign Up to like & getrecommendations! Published in 2017 at "Comptes Rendus Mathematique"
DOI: 10.1016/j.crma.2017.04.009
Abstract: Abstract In this paper, we study the chemotaxis system: { u t = ∇ ⋅ ( ξ ∇ u − χ u ∇ v ) , x ∈ Ω , t > 0 , v… read more here.
Keywords: consumption chemoattractant; solutions chemotaxis; classical solutions; chemotaxis model ... See more keywords
On the global classical solutions for the generalized SQG equation
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2022.109503
Abstract: In this paper, we study the existence of global classical solutions to the generalized surface quasi-geostrophic equation. By using the variational method, we provide some new families of global classical solutions for to the generalized… read more here.
Keywords: generalized sqg; sqg equation; classical solutions; global classical ... See more keywords
On classical solutions to the Hartree equation
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.123859
Abstract: Abstract This paper is concerned with positive classical solutions to the Hartree equation − Δ u = ( 1 | x | n − α ⁎ u p ) u p − 1 in R… read more here.
Keywords: equation; hartree equation; classical solutions; solutions hartree ... See more keywords
Classical solutions of oblique derivative problem in nonsmooth domains with mean Dini coefficients
Sign Up to like & getrecommendations! Published in 2020 at "Transactions of the American Mathematical Society"
DOI: 10.1090/tran/8042
Abstract: We consider second-order elliptic equations in nondivergence form with oblique derivative boundary conditions. We show that any strong solutions to such problems are twice continuously differentiable up to the boundary when the boundary can be… read more here.
Keywords: problem nonsmooth; solutions oblique; nonsmooth domains; oblique derivative ... See more keywords
The classical solutions with k− = 0 in Kaku theory
Sign Up to like & getrecommendations! Published in 2023 at "Progress of Theoretical and Experimental Physics"
DOI: 10.1093/ptep/ptad069
Abstract: We consider Kaku theory introduced in [1] and investigate classical solutions. In particular, we obtain that the equation of motion with the restriction k− = 0 in the Kaku theory is equivalent to the equation of motion… read more here.
Keywords: theory; solutions kaku; equation motion; classical solutions ... See more keywords
Classical Solutions of Hyperbolic Equations with Nonlocal Potentials
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DOI: 10.1134/s1064562421030157
Abstract: A three-parameter family of global solutions for a two-dimensional hyperbolic differential-difference equation with a nonlocal potential is constructed. A theorem that the obtained solutions are classical is proved. read more here.
Keywords: nonlocal potentials; solutions hyperbolic; equations nonlocal; hyperbolic equations ... See more keywords
Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
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DOI: 10.3390/e24121829
Abstract: This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term −Δu=f(x,u,∇u) on Ω restricted by the boundary condition u|∂Ω=0, where Ω is a bounded domain in RN with sufficiently… read more here.
Keywords: solutions nonlinear; elliptic equations; nonlinear elliptic; classical solutions ... See more keywords
Classical Solutions for the Generalized Kawahara–KdV System
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DOI: 10.3390/sym15061159
Abstract: In this article, we investigate the generalized Kawahara–KdV system. A new topological approach is applied to prove the existence of at least one classical solution and at least two non-negative classical solutions. The arguments are… read more here.
Keywords: classical solutions; kdv system; generalized kawahara; kawahara kdv ... See more keywords